Journal of Generalized Lie Theory and Applications Articles (Project Euclid)
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The latest articles from Journal of Generalized Lie Theory and Applications on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Fri, 06 Aug 2010 10:55 EDTFri, 06 Aug 2010 10:56 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Notes on cohomologies of ternary algebras of associative type
http://projecteuclid.org/euclid.jglta/1281106534
<strong>H. Ataguema</strong>, <strong>A. Makhlouf</strong><p><strong>Source: </strong>J. Gen. Lie Theory Appl., Volume 3, Number 3, 157--174.</p><p><strong>Abstract:</strong><br/>
The aim of this paper is to investigate the cohomologies for ternary algebras of
associative type. We study in particular the cases of partially associative
ternary algebras and weak totally associative ternary algebras. Also, we
consider the Takhtajan's construction, which was used to construct a cohomology
of ternary Nambu-Lie algebras using Chevalley-Eilenberg cohomology of Lie
algebras, and discuss it in the case of ternary algebras of associative type.
One of the main results of this paper states that a usual deformation cohomology
does not exist for partially associative ternary algebras which implies that
their operad is not a Koszul operad.
</p>projecteuclid.org/euclid.jglta/1281106534_Fri, 06 Aug 2010 10:55 EDTFri, 06 Aug 2010 10:55 EDTNoncommutative Geometry and Dynamical Models on $U(u(2))$ Backgroundhttp://projecteuclid.org/euclid.jglta/1443617955<strong>D Gurevich</strong>, <strong>P Saponov</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 10 pages.</p><p><strong>Abstract:</strong><br/>
In our previous publications we have introduced a differential calculus on the
algebra $U(gl(m))$ based on a new form of the Leibniz rule which differs from
that usually employed in Noncommutative Geometry. This differential calculus
includes partial derivatives in generators of the algebra $U(gl(m))$ and their
differentials. The corresponding differential algebra $Ω(U(gl(m)))$ is a
deformation of the commutative algebra $Ω(\operatorname{Sym}(gl(m)))$. A similar
claim is valid for the Weyl algebra $W(U(gl(m)))$ generated by the algebra
$U(gl(m))$ and the mentioned partial derivatives. In the particular case m=2 we
treat the compact form $U(u(2))$ of this algebra as a quantization of the
Minkowski space algebra. Below, we consider non-commutative versions of the
Klein-Gordon equation and the Schrodinger equation for the hydrogen atom. To
this end we de ne an extension of the algebra $U(u(2))$ by adding to it
meromorphic functions in the so-called quantum radius and quantum time. For the
quantum Klein-Gordon model we get (under an assumption on momenta) an analog of
the plane wave, for the quantum hydrogen atom model we find the first order
corrections to the ground state energy and the wave function.
</p>projecteuclid.org/euclid.jglta/1443617955_20150930085917Wed, 30 Sep 2015 08:59 EDTHelgason-Schiman Formula for Semisimple Lie Groups of Arbitrary Rankhttp://projecteuclid.org/euclid.jglta/1443617956<strong>UN Bassey</strong>, <strong>OO Oyadare</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 6 pages.</p><p><strong>Abstract:</strong><br/>
This paper extends the Helgason-Schiffman formula for the H-function on a
semisimple Lie group of real rank one to cover a semisimple Lie group G of
arbitrary real rank. A set of analytic $\mathbb{R}$ -valued cocycles are deduced
for certain real rank one subgroups of G. This allows a formula for the
c-function on G to be worked out as an integral of a product of their
resolutions on the summands in a direct-sum decomposition of the maximal abelian
subspace of the Lie algebra g of G. Results about the principal series of
representations of the real rank one subgroups are also obtained, among other
things.
</p>projecteuclid.org/euclid.jglta/1443617956_20150930085917Wed, 30 Sep 2015 08:59 EDTThe $m$-Derivations of Distribution Lie Algebrashttp://projecteuclid.org/euclid.jglta/1443617957<strong>Princy Randriambololondrantomalala</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 6 pages.</p><p><strong>Abstract:</strong><br/>
Let $M$ be a N-dimensional smooth differentiable manifold. Here, we are going to
analyze $(m>1)$-derivations of Lie algebras relative to an involutive
distribution on subrings of real smooth functions on $M$. First, we prove that
any $(m>1)$-derivations of a distribution $Ω$ on the ring of real
functions on $M$ as well as those of the normalizer of $Ω$ are Lie derivatives
with respect to one and only one element of this normalizer, if $Ω$ doesn’t
vanish everywhere. Next, suppose that $N = n + q$ such that $n>0$, and
let $S$ be a system of $q$ mutually commuting vector fields. The Lie algebra of
vector fields ${\mathfrak{A}_s}$ on $M$ which commutes with $S$, is a
distribution over the ring $F_0(M)$ of constant real functions on the leaves
generated by $S$. We find that $m$-derivations of ${\mathfrak{A}_s}$ is local if
and only if its derivative ideal coincides with ${\mathfrak{A}_s}$ itself. Then,
we characterize all non local $m$-derivation of ${\mathfrak{A}_s}$. We prove
that all $m$-derivations of ${\mathfrak{A}_s}$ and the normalizer of
${\mathfrak{A}_s}$ are derivations. We will make these derivations and those of
the centralizer of ${\mathfrak{A}_s}$ more explicit.
</p>projecteuclid.org/euclid.jglta/1443617957_20150930085917Wed, 30 Sep 2015 08:59 EDTFour-Dimensional Nilpotent Diassociative Algebrashttp://projecteuclid.org/euclid.jglta/1443617958<strong>W Basri</strong>, <strong>IS Rakhimov</strong>, <strong>IM Rikhsiboev</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 6 pages.</p><p><strong>Abstract:</strong><br/>
The paper is devoted to structural properties of diassociative algebras. We
introduce the notions of nilpotency, solvability of the diassociative algebras
and study their properties. The list of all possible nilpotent diassociative
algebra structures on four-dimensional complex vector spaces is given.
</p>projecteuclid.org/euclid.jglta/1443617958_20150930085917Wed, 30 Sep 2015 08:59 EDTTraffic Network and Optimization a Future Subscriber’s Mobile Telecom Operator in
Trainhttp://projecteuclid.org/euclid.jglta/1443617959<strong>J Allami</strong>, <strong>H Ez-Zahraouy</strong>, <strong>A Benyoussef</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 6 pages.</p><p><strong>Abstract:</strong><br/>
In this work, we studied the behavior and mobility of telecom subscribers into a
train for now and predict a future telecom movement subscriber and have a
perfect resources data signal of an operator mobile telecom, we used a
deterministic and a probabilistic method. the train in our model example travels
through a cellular network and passed into four zones (Z1, Z2, Z3 and Z4), each
one is characterized by: topography, numbers of the cellular network, types of
network (GSM, GPRS, UMTS ...), numbers of subscribers, types of
subscribers(staffs, students, workers and others), numbers of operators
(Operator 1, Operator 2 and Operator 3). We have studied statistics in
deterministic and probabilistic vision of traffic telecom; the model used is
approach to vehicular traffic model.
</p>projecteuclid.org/euclid.jglta/1443617959_20150930085917Wed, 30 Sep 2015 08:59 EDTOn The Stability of Conditional Homomorphisms in Lie $C$^*$-algebrashttp://projecteuclid.org/euclid.jglta/1443617960<strong>M Eshaghi</strong>, <strong>S Abbaszadeh</strong>, <strong>Manuel De la Sen</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 5 pages.</p><p><strong>Abstract:</strong><br/>
During the last years several papers studying conditional functional equations
have appeared. They mostly deal with equations satisfied on some restricted
domain and many among them concern equations postulated for orthogonal vectors.
In this paper, we define the conditional homomorphisms with the predecessor
defined by $\gamma(x)=\gamma(y) with an even mapping $\gamma$. Then, using a
fixed point theorem, we investigate the stability of the conditional
homomorphisms in Lie $C^*$-algebras.
</p>projecteuclid.org/euclid.jglta/1443617960_20150930085917Wed, 30 Sep 2015 08:59 EDTNon-Commutative Ternary Nambu-Poisson Algebras and Ternary Hom-Nambu-Poisson
Algebrashttp://projecteuclid.org/euclid.jglta/1443617961<strong>A Makhlouf</strong>, <strong>A Amri</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 8 pages.</p><p><strong>Abstract:</strong><br/>
The main purpose of this paper is to study non-commutative ternary Nambu-Poisson
algebras and their Homtype version. We provide construction results dealing with
tensor product and direct sums of two (non- commutative) ternary (Hom-)
Nambu-Poisson algebras. Moreover, we explore twisting principle of
(non-commutative) ternary Nambu-Poisson algebras along with algebra morphism
that lead to construct (non-commutative) ternary Hom- Nambu-Poisson algebras.
Furthermore, we provide examples and a 3-dimensional classification of
non-commutative ternary Nambu-Poisson algebras.
</p>projecteuclid.org/euclid.jglta/1443617961_20150930085917Wed, 30 Sep 2015 08:59 EDTComplete Left-Invariant Affine Structures on Solvable Non-Unimodular
Three-Dimensional Lie Groupshttp://projecteuclid.org/euclid.jglta/1443617962<strong>M Guediri</strong>, <strong>K Al-Balawi</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 11 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we shall use a method based on the theory of extensions of
left-symmetric algebras to classify complete left-invariant affine real
structures on solvable non-unimodular three-dimensional Lie groups.
</p>projecteuclid.org/euclid.jglta/1443617962_20150930085917Wed, 30 Sep 2015 08:59 EDTLocally Compact Homogeneous Spaces with Inner Metrichttp://projecteuclid.org/euclid.jglta/1443617963<strong>VN Berestovskii</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 6 pages.</p><p><strong>Abstract:</strong><br/>
The author reviews his results on locally compact homogeneous spaces with inner
metric, in particular, homogeneous manifolds with inner metric. The latter are
isometric to homogeneous (sub-) Finslerian manifolds; under some additional
conditions they are isometric to homogeneous (sub)-Riemannian manifolds. The
class Ω of all locally compact homogeneous spaces with inner metric is supplied
with some metric $d_{BGH}$ such that 1) $(Ω, d_{BGH})$ is a complete metric
space; 2) a sequences in $(Ω, d_{BGH})$ is converging if and only if it is
converging in Gromov-Hausdor sense; 3) the subclasses M of homogeneous manifolds
with inner metric and L G of connected Lie groups with leftinvariant Finslerian
metric are everywhere dense in $(Ω, d_{BGH})$: It is given a metric
characterization of Carnot groups with left-invariant sub-Finslerian metric. At
the end are described homogeneous manifolds such that any invariant inner metric
on any of them is Finslerian.
</p>projecteuclid.org/euclid.jglta/1443617963_20150930085917Wed, 30 Sep 2015 08:59 EDTOn Remarkable Relations and the Passage to the Limit in the Theory of Infinite
Systemshttp://projecteuclid.org/euclid.jglta/1443617964<strong>FM Fedorov</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 9 pages.</p><p><strong>Abstract:</strong><br/>
The present paper is about the problem of the passage to the limit from finite
truncated systems to infinite system of linear algebraic equations. We consider
the four important relations that arise in dealing with finite truncated
Gaussian systems. These remarkable relations in fact give the opportunity to
make transition from the solutions of finite systems to the solution of infinite
system.
</p>projecteuclid.org/euclid.jglta/1443617964_20150930085917Wed, 30 Sep 2015 08:59 EDTEuler-Poincare Formalism of Peakon Equations with Cubic Nonlinearityhttp://projecteuclid.org/euclid.jglta/1443617965<strong>P Guha</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 7 pages.</p><p><strong>Abstract:</strong><br/>
We present an Euler-Poincaré (EP) formulation of a new class of peakon equations
with cubic nonlinearity, viz., Fokas-Qiao and V. Novikov equations, in two
almost equivalent ways. The first method is connected to flows on the spaces of
Hill’s and first order differential operator and the second method depends
heavily on the flows on space of tensor densities. We give a comparative
analysis of these two methods. We show that the Hamiltonian structures obtained
by Qiao and Hone and Wang can be reproduced by EP formulation. We outline the
construction for the 2+1-dimensional generalization of the peakon equations with
cubic nonlinearity using the action of the loop extension of Vect(S1) on the
space of tensor densities.
</p>projecteuclid.org/euclid.jglta/1443617965_20150930085917Wed, 30 Sep 2015 08:59 EDTSome Generalized Hom-Algebra Structureshttp://projecteuclid.org/euclid.jglta/1443617966<strong>I Bakayoko</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 7 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we introduce generalized left-Hom-symmetric algebras and
generalized Hom-dendriform algebras as well as the corresponding modules. We
investigate the connection between these categories of generalized Homalgebras
and modules. We give various constructions of these generalized Hom-algebra
structures from either a given one or an ordinary one. We prove that any
generalized Hom-dialgebras give rise to generalized Hom-Leibniz-Poisson algebras
and generalized Hom-Poisson dialgebras.
</p>projecteuclid.org/euclid.jglta/1443617966_20150930085917Wed, 30 Sep 2015 08:59 EDTMeander Graphs and Frobenius Seaweed Lie Algebras IIhttp://projecteuclid.org/euclid.jglta/1443617967<strong>Vincent Coll</strong>, <strong>Matthew Hyatt</strong>, <strong>Colton Magnant</strong>, <strong>Hua Wang</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 7 pages.</p><p><strong>Abstract:</strong><br/>
We provide a recursive classification of meander graphs, showing that each
meander is identified by a unique sequence of fundamental graph theoretic moves.
This sequence is called the meander’s signature and can be used to construct
arbitrarily large sets of meanders, Frobenius or otherwise, of any size and
configuration. In certain special cases, the signature is used to produce an
explicit formula for the index of seaweed Lie subalgebra of sl(n) in terms of
elementary functions.
</p>projecteuclid.org/euclid.jglta/1443617967_20150930085917Wed, 30 Sep 2015 08:59 EDTA Survey of My Recent Researchhttp://projecteuclid.org/euclid.jglta/1443617968<strong>N Kamiya</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 1 page.</p>projecteuclid.org/euclid.jglta/1443617968_20150930085917Wed, 30 Sep 2015 08:59 EDTHigher Bruhat and Tamari Orders and their Realizationshttp://projecteuclid.org/euclid.jglta/1443617969<strong>A Dimakis</strong>, <strong>F Müller-Hoissen</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 1, 3 pages.</p>projecteuclid.org/euclid.jglta/1443617969_20150930085917Wed, 30 Sep 2015 08:59 EDTVerification of Some Properties of the C-nilpotent Multiplier in Lie
Algebrashttp://projecteuclid.org/euclid.jglta/1454422003<strong>Sadeghieh A</strong>, <strong>Araskhan M</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 2, 3 pages.</p><p><strong>Abstract:</strong><br/>
The purpose of this paper is to obtain some inequalities and certain bounds for
the dimension of the c-nilpotent multiplier of finite dimensional nilpotent Lie
algebras and their factor Lie algebras. Also, we give an inequality for the
dimension of the c-nilpotent multiplier of L connected with dimension of the Lie
algebras ${\gamma _d}(L)$ and $L/{Z_{d - 1}}(L)$. Finally, we compare our
results with the previously known result.
</p>projecteuclid.org/euclid.jglta/1454422003_20160202090650Tue, 02 Feb 2016 09:06 ESTMatrix Lie Groups: An Introductionhttp://projecteuclid.org/euclid.jglta/1454422004<strong>Lawson J</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 2, 9 pages.</p><p><strong>Abstract:</strong><br/>
This article presents basic notions of Lie theory in the context of matrix groups
with goals of minimizing the required mathematical background and maximizing
accessibility. It is structured with exercises that enhance the text and make
the notes suitable for (part of) an introductory course at the upper level
undergraduate or early graduate level. Indeed the notes were originally written
as part of an introductory course to geometric control theory.
</p>projecteuclid.org/euclid.jglta/1454422004_20160202090650Tue, 02 Feb 2016 09:06 ESTAlgebra, Hyperalgebra and Lie-Santilli Theoryhttp://projecteuclid.org/euclid.jglta/1454422005<strong>Davvaza B</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 2, 5 pages.</p><p><strong>Abstract:</strong><br/>
The theory of hyperstructures can offer to the Lie-Santilli Theory a variety of
models to specify the mathematical representation of the related theory. In this
paper we focus on the appropriate general hyperstructures, especially on
hyperstructures with hyperunits. We define a Lie hyperalgebra over a hyperfield
as well as a Jordan hyperalgebra, and we obtain some results in this respect.
Finally, by using the concept of fundamental relations we connect hyper algebras
to Lie algebras and Lie-Santilli-addmissible algebras.
</p>projecteuclid.org/euclid.jglta/1454422005_20160202090650Tue, 02 Feb 2016 09:06 ESTLie Group Method for Studying the Heat Generation Effect on Freeconvection
Laminar Boundary-layer Flow Over a Vertical Flat Platehttp://projecteuclid.org/euclid.jglta/1454422006<strong>Abd-el-Malek MB</strong>, <strong>Badran NA</strong>, <strong>Hassan HS</strong>, <strong>Abbas HH</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 2, 9 pages.</p><p><strong>Abstract:</strong><br/>
The nonlinear equations of heat and mass transfer in two-dimensional
free-convection, laminar, boundary layer flow of a viscous incompressible fluid
over a vertical plate with thermophoresis and heat generation effect have been
considered. We apply Lie-group method for determining symmetry reductions of
partial differential equations. Liegroup method starts out with a general
infinitesimal group of transformations under which the given partial
differential equations are invariant. The determining equations are a set of
linear differential equations, the solution of which gives the transformation
function or the infinitesimals of the dependent and independent variables. After
the group has been determined, a solution to the given partial differential
equations may be found from the invariant surface condition such that its
solution leads to similarity variables that reduce the number of independent
variables of the system. The effect of the heat generation parameter He, the
Prandtl number Pr, the Schimted number Sc, the thermophoretic parameter $\tau $,
the solutal Grashof number Gc and the thermal Grashof number Gr on velocity,
concentration and temperature have been studied and the results are plotted.
</p>projecteuclid.org/euclid.jglta/1454422006_20160202090650Tue, 02 Feb 2016 09:06 ESTLoops in Noncompact Groups of Hermitian Symmetric Type and Factorizationhttp://projecteuclid.org/euclid.jglta/1454422007<strong>Caine A</strong>, <strong>Pickrell D</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 2, 14 pages.</p><p><strong>Abstract:</strong><br/>
In studies of Pittmann, we showed that a loop in a simply connected compact Lie
group has a unique Birkhoff (or triangular) factorization if and only if the
loop has a unique root subgroup factorization (relative to a choice of a reduced
sequence of simple reflections in the affine Weyl group). In this paper our main
purpose is to investigate Birkhoff and root subgroup factorization for loops in
a noncompact semisimple Lie group of Hermitian symmetric type. In literature of
caine, we showed that for an element of, i.e. a constant loop, there is a unique
Birkhoff factorization if and only if there is a root subgroup factorization.
However for loops in, while a root subgroup factorization implies a unique
Birkhoff factorization, the converse is false. As in the compact case, root
subgroup factorization is intimately related to factorization of Toeplitz
determinants.
</p>projecteuclid.org/euclid.jglta/1454422007_20160202090650Tue, 02 Feb 2016 09:06 ESTGeneralizing Two Structure Theorems of Lie Algebras to the Fuzzy Lie
Algebrashttp://projecteuclid.org/euclid.jglta/1454422008<strong>da Motta Ferreira João Carlos</strong>, <strong>Bruno Marietto Maria das Graças</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 2, 4 pages.</p><p><strong>Abstract:</strong><br/>
In this paper we generalize two structure theorems of the class of Lie algebras
to the class of fuzzy Lie algebras, namely the structure theorem of semisimple
Lie algebras and the Levi’s decomposition theorem. Some open questions are also
given.
</p>projecteuclid.org/euclid.jglta/1454422008_20160202090650Tue, 02 Feb 2016 09:06 ESTA Class of Nonassociative Algebras Including Flexible and Alternative Algebras,
Operads and Deformationshttp://projecteuclid.org/euclid.jglta/1454422009<strong>Remm E</strong>, <strong>Goze M</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 2, 6 pages.</p><p><strong>Abstract:</strong><br/>
There exists two types of nonassociative algebras whose associator satisfies a
symmetric relation associated with a 1-dimensional invariant vector space with
respect to the natural action of the symmetric group ${\Sigma _3}$. The first
one corresponds to the Lie-admissible algebras and this class has been studied
in a previous paper of Remm and Goze. Here we are interested by the second one
corresponding to the third power associative algebras.
</p>projecteuclid.org/euclid.jglta/1454422009_20160202090650Tue, 02 Feb 2016 09:06 ESTLie Group Analysis for Solving the Problem of Diffusion of Drugs across a
Biological Membranehttp://projecteuclid.org/euclid.jglta/1454422010<strong>Abd-el-Malek MB</strong>, <strong>Amin AM</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 2, 4 pages.</p><p><strong>Abstract:</strong><br/>
The Lie group method is applied to study the diffusion process of drugs across a
biological membrane which tends to partially absorb the drug. For the diffusion
coefficient, we considered two cases. The Lie group analysis is based on
reducing the number of independent variables by one, and consequently the
mathematical model described by nonlinear partial differential equation to,
covers the diffusion process with the boundary and initial conditions, and is
transformed into an ordinary differential equation with the corresponding
conditions. The obtained nonlinear ordinary differential equation is solved
numerically using the ${4^{th}}$ and ${5^{th}}$ Runge Kutta method, and the
results are illustrated graphically and in tables too.
</p>projecteuclid.org/euclid.jglta/1454422010_20160202090650Tue, 02 Feb 2016 09:06 ESTA Prime Radical of Weakly Artinian Ω-Groups with Finite Condition is Locally
Nilpotenthttp://projecteuclid.org/euclid.jglta/1454422011<strong>Blagovisnaya A</strong>, <strong>Pikhtilkov S</strong>, <strong>Pikhtilkova O</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 2, 2 pages.</p><p><strong>Abstract:</strong><br/>
First we discuss the background of the issue to Lie algebras. We also show the
relationship of our problem and A.V. Mikhalev’s problem. The main result is
proved for Lie algebras. We then consider the $\Omega $-group".
</p>projecteuclid.org/euclid.jglta/1454422011_20160202090650Tue, 02 Feb 2016 09:06 ESTSome Aspects of Semi-Abelian Homology and Protoadditive Functorshttp://projecteuclid.org/euclid.jglta/1454422012<strong>Everaert T</strong>, <strong>Gran M</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number 2, 3 pages.</p><p><strong>Abstract:</strong><br/>
In this note some recent developments in the study of homology in semi-abelian
categories are briefly presented. In particular the role of protoadditive
functors in the study of Hopf formulae for homology is explained.
</p>projecteuclid.org/euclid.jglta/1454422012_20160202090650Tue, 02 Feb 2016 09:06 ESTOn the Representation Spaces of the Jordanian Planehttp://projecteuclid.org/euclid.jglta/1478833219<strong>Natalia K Iyudu</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number S1, 2 pages.</p>projecteuclid.org/euclid.jglta/1478833219_20161110220033Thu, 10 Nov 2016 22:00 ESTEggert's Conjecture for 2-Generated Nilpotent Algebrashttp://projecteuclid.org/euclid.jglta/1478833220<strong>Miroslav Korbelar</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number S1, 3 pages.</p><p><strong>Abstract:</strong><br/>
Let A be a commutative nilpotent finitely-dimensional algebra over a field $F$ of
characteristic $p > 0$. A conjecture of Eggert says that $p^.
\operatorname{dim} A^{(p)} \operatorname{dim} A$, where $A^{(p)}$ is the
subalgebra of $A$ generated by elements $a^p , a ∈ A$. We show that the
conjecture holds if $A^{(p)}$ is at most 2-generated.
</p>projecteuclid.org/euclid.jglta/1478833220_20161110220033Thu, 10 Nov 2016 22:00 ESTKazhdan Lusztig Cells in Infinite Coxeter Groupshttp://projecteuclid.org/euclid.jglta/1478833221<strong>MV Belolipetsky</strong>, <strong>PE Gunnells</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number S1, 4 pages.</p><p><strong>Abstract:</strong><br/>
Groups defined by presentations of the form $\langle s_1,\ldots,s_n | s_i^2 = 1,
(s_is_j)^{m_{ij}} = 1(i,j=1,\ldots,n)\rangle$ are called Coxeter groups. The
exponents $m_{i,j} ∈ N ∪ {∞}$ form the Coxeter matrix, which characterizes the
group up to isomorphism. The Coxeter groups that are most important for
applications are the Weyl groups and affine Weyl groups. For example, the
symmetric group $S_n$ is isomorphic to the Coxeter group with presentation
$\langle s_1,\ldots,s_n | s_i^2 = 1
(i=1,\ldots,n),(s_is_{i+1})^3=1(i=1,\ldots,n-1)\rangle$, and is also known as
the Weyl group of type $A_{n-1}$.
</p>projecteuclid.org/euclid.jglta/1478833221_20161110220033Thu, 10 Nov 2016 22:00 ESTJordan delta-Derivations of Associative Algebrashttp://projecteuclid.org/euclid.jglta/1478833222<strong>Ivan Kaygorodov</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number S1, 3 pages.</p><p><strong>Abstract:</strong><br/>
We described the structure of jordan $δ$-derivations and jordan
$δ$-prederivations of unital associative algebras. We gave examples of nonzero
jordan 1/2 -derivations, but not 1/2 -derivations.
</p>projecteuclid.org/euclid.jglta/1478833222_20161110220033Thu, 10 Nov 2016 22:00 ESTA Multivariate Weight Enumerator for Tail-biting Trellis Pseudocodewordshttp://projecteuclid.org/euclid.jglta/1478833223<strong>Nigel Boston</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number S1, 4 pages.</p><p><strong>Abstract:</strong><br/>
Tail-biting-trellis representations of codes allow for iterative decoding
algorithms, which are limited in effectiveness by the presence of
pseudocodewords. We introduce a multivariate weight enumerator that keeps track
of these pseudocodewords. This enumerator is invariant under many linear
transformations, often enabling us to compute it exactly. The extended binary
Golay code has a particularly nice tail-biting-trellis and a famous unsolved
question is to determine its minimal AWGN pseudodistance. The new enumerator
provides an inroad to this problem.
</p>projecteuclid.org/euclid.jglta/1478833223_20161110220033Thu, 10 Nov 2016 22:00 ESTHardy Spaces on Compact Riemann Surfaces with Boundaryhttp://projecteuclid.org/euclid.jglta/1478833224<strong>A Zuevsky</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number S1, 8 pages.</p><p><strong>Abstract:</strong><br/>
We consider the holomorphic unramified mapping of two arbitrary finite bordered
Riemann surfaces. Extending the map to the doubles $X_1$ and $X_2$ of Riemann
surfaces we define the vector bundle on the second double as a direct image of
the vector bundle on first double. We choose line bundles of half-order
differentials $Δ_1$ and $Δ_2$ so that the vector bundle $V_{\chi_2}^{X_2}⊗Δ_2$
on $X_2$ would be the direct image of the vector bundle $V_{\chi_1}^{X_1}⊗Δ_2$.
We then show that the Hardy spaces $H_{2,J_1(p)}(S_1,V_{χ_1}⊗Δ_1$ and
$H_{2,J_2(p)}(S_2,V_{χ_2}⊗Δ_2$ are isometrically isomorphic. Proving that we
construct an explicit isometric isomorphism and a matrix representation $χ_2$ of
the fundamental group $π_1(X_2, p_0)$ given a matrix representation $χ_1$ of the
fundamental group $π_1(X_1, p'_0)$. On the basis of the results of Alpay et al.
and Theorem 3.1 proven in the present work we then conjecture that there exists
a covariant functor from the category $\mathcal{RH}$ of finite bordered surfaces
with vector bundle and signature matrices to the category of Kreĭn spaces and
isomorphisms which are ramified covering of Riemann surfaces.
</p>projecteuclid.org/euclid.jglta/1478833224_20161110220033Thu, 10 Nov 2016 22:00 EST$N$-Complex, Graded $q$-Differential Algebra and $N$-Connection on
Moduleshttp://projecteuclid.org/euclid.jglta/1478833225<strong>Viktor Abramov</strong>, <strong>Olga Liivapuu</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number S1, 11 pages.</p><p><strong>Abstract:</strong><br/>
It is well known that given a differential module $E$ with a differential d we
can measure the non-exactness of this differential module by its homologies
which are based on the key relation $d^2 =0$. This relation is a basis for
several important structures in modern mathematics and theoretical physics to
point out only two of them which are the theory of de Rham cohomologies on
smooth manifolds and the apparatus of BRST-quantization in gauge field
theories.
</p>projecteuclid.org/euclid.jglta/1478833225_20161110220033Thu, 10 Nov 2016 22:00 ESTOrthogonal Matrix Invariantshttp://projecteuclid.org/euclid.jglta/1478833226<strong>AA Lopatin</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number S1, 3 pages.</p><p><strong>Abstract:</strong><br/>
The orthogonal group acts on the space of several $n × n$ matrices by
simultaneous conjugation. For an infinite field of characteristic different from
two, relations between generators for the algebra of invariants are described.
As an application, the maximal degree of elements of a minimal system of
generators is described with deviation 3.
</p>projecteuclid.org/euclid.jglta/1478833226_20161110220033Thu, 10 Nov 2016 22:00 ESTKaplansky's Type Constructions for Weak Bialgebras and Weak Hopf Algebrashttp://projecteuclid.org/euclid.jglta/1478833227<strong>Z Chebel</strong>, <strong>A Makhlouf</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number S1, 9 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we study weak bialgebras and weak Hopf algebras. These algebras
form a class wider than bialgebras respectively Hopf algebras. The main results
of this paper are Kaplansky’s type constructions which lead to weak bialgebras
or weak Hopf algebras starting from a regular algebra or a bialgebra. Also we
provide a classification of 2-dimensional and 3-dimensional weak bialgebras and
weak Hopf algebras. We determine then the stabilizer group and the
representative of these classes, the action being that of the linear group.
</p>projecteuclid.org/euclid.jglta/1478833227_20161110220033Thu, 10 Nov 2016 22:00 ESTExistence Theorems in Linear Chaoshttp://projecteuclid.org/euclid.jglta/1478833228<strong>Stanislav Shkarin</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 9, Number S1, 34 pages.</p><p><strong>Abstract:</strong><br/>
Chaotic linear dynamics deals primarily with various topological ergodic
properties of semigroups of continuous linear operators acting on a topological
vector space. In this survey paper, we treat questions of characterizing which
of the spaces from a given class support a semigroup of prescribed shape
satisfying a given topological ergodic property.
In particular, we characterize countable inductive limits of separable Banach
spaces that admit a hypercyclic operator, show that there is a non-mixing
hypercyclic operator on a separable infinite dimensional complex Fréchet space
$X$ if and only if $X$ is non-isomorphic to the space $ω$ of all sequences with
coordinatewise convergence topology. It is also shown for any $k ∈ \mathbb{N}$,
any separable infinite dimensional Fréchet space $X$ non-isomorphic to $ω$
admits a mixing uniformly continuous group $\{T_t\}_{t∈C^n}$ of continuous linear
operators and that there is no supercyclic strongly continuous operator
semigroup $\{T_t\}_{t≥0}$ on $ω$. We specify a wide class of Fréchet spaces $X$,
including all infinite dimensional Banach spaces with separable dual, such that
there is a hypercyclic operator $T$ on $X$ for which the dual operator $T′$ is
also hypercyclic. An extension of the Salas theorem on hypercyclicity of a
perturbation of the identity by adding a backward weighted shift is presented
and its various applications are outlined.
</p>projecteuclid.org/euclid.jglta/1478833228_20161110220033Thu, 10 Nov 2016 22:00 ESTChief Factors of Lie Algebrashttp://projecteuclid.org/euclid.jglta/1479265219<strong>DA Towers</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number S2, 3 pages.</p><p><strong>Abstract:</strong><br/>
In group theory the chief factors allow a group to be studied by its representation theory on particularly natural
irreducible modules. It is to be expected, therefore, that they will play an important role in the study of Lie algebras. In
this article we survey a few of their properties.
</p>projecteuclid.org/euclid.jglta/1479265219_20161115220026Tue, 15 Nov 2016 22:00 ESTJet Bundles on Projective Space IIhttp://projecteuclid.org/euclid.jglta/1479265220<strong>H Maakestad</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number S2, 13 pages.</p><p><strong>Abstract:</strong><br/>
In previous papers the structure of the jet bundle as $P$-module has been studied using different techniques. In
this paper we use techniques from algebraic groups, sheaf theory, generliazed Verma modules, canonical filtrations
of irreducible $\mathrm{SL}(V)$-modules and annihilator ideals of highest weight vectors to study the canonical filtration
$U_l(\mathfrak{g})L^d$
of the irreducible $\mathrm{SL}(V)$-module $\mathrm{H}^0 (X,\mathcal{O}_X(d))^*$ where $X = \mathbb{G}(m, m + n)$. We study
$U_l(\mathfrak{g})L^d$
using results from previous
papers on the subject and recover a well known classification of the structure of the jet bundle $\mathcal{P}^l(\mathcal{O}(d))$ on projective
space $\mathcal{P}^l(\mathcal{O}_X(V*))$ as $P$-module. As a consequence we prove formulas on the splitting type of the jet bundle on projective
space as abstract locally free sheaf. We also classify the $P$-module of the first order jet bundle
$\mathcal{P}_X^1(\mathcal{O}_X(d))$ for any $d
≥ 1$. We study the incidence complex for the line bundle $\mathcal{O}(d)$ on the projective line and show it is a resolution of the
ideal sheaf of $I^l (\mathcal{O}_X(d))$ - the incidence scheme of $\mathcal{O}_X(d)$. The aim of the study is to apply it to the study of syzygies of
discriminants of linear systems on projective space and grassmannians.
</p>projecteuclid.org/euclid.jglta/1479265220_20161115220026Tue, 15 Nov 2016 22:00 ESTThe $m$-Derivations of Analytic Vector Fields Lie Algebrashttp://projecteuclid.org/euclid.jglta/1479265221<strong>P Randriambololondrantomalala </strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number S2, 5 pages.</p><p><strong>Abstract:</strong><br/>
We consider a (real or complex) analytic manifold $M$. Assuming that $F$ is a ring of all analytic functions, full
or truncated with respect to the local coordinates on $M$; we study the $(m ≥ 2)$-derivations of all involutive analytic
distributions over $F$ and their respective normalizers.
</p>projecteuclid.org/euclid.jglta/1479265221_20161115220026Tue, 15 Nov 2016 22:00 ESTThe Generalization of the Stallings Theoremhttp://projecteuclid.org/euclid.jglta/1479265222<strong>A Onsory</strong>, <strong>M Araskhan</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number S2, 3 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we present a relative version of the concept of lower marginal series and give some isomorphisms
among $\mathcal{V}G$-marginal factor groups. Also, we conclude a generalized version of the Stalling’s theorem. Finally, we
present a sufficient condition under which the order of the generalized Baer-invariant of a pair of finite groups divides
the order of the generalized Baer-invariant of its factor groups.
</p>projecteuclid.org/euclid.jglta/1479265222_20161115220026Tue, 15 Nov 2016 22:00 ESTSelf-adjointness, Group Classification and Conservation Laws of an Extended Camassa-Holm Equationhttp://projecteuclid.org/euclid.jglta/1479265223<strong>M Nadjafikhah</strong>, <strong>N Pourrostami</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number S2, 5 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we prove that equation $E ≡ u_1-u_{_x2_t}+u_xf(u)-au_xu_{}x^2-buu_{x^3}=0$ is self-adjoint and quasi self-adjoint,
then we construct conservation laws for this equation using its symmetries. We investigate a symmetry classification
of this nonlinear third order partial differential equation, where $f$ is smooth function on $u$ and $a$, $b$ are arbitrary constans.
We find Three special cases of this equation, using the Lie group method.
</p>projecteuclid.org/euclid.jglta/1479265223_20161115220026Tue, 15 Nov 2016 22:00 ESTOn Representations of Bol Algebrashttp://projecteuclid.org/euclid.jglta/1479265224<strong>N Ndoune</strong>, <strong>T Bouetou Bouetou</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number S2, 6 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we introduce the notion of representation of Bol algebra. We prove an analogue of the classical
Engel’s theorem and the extension of Ado-Iwasawa theorem for Bol Algebras. We study the category of representations
of Bol algebras and show that it is a tensor category. In the case of regular representations of Bol algebras, we give
a complete classification of them for all two-dimensional Bol algebras.
</p>projecteuclid.org/euclid.jglta/1479265224_20161115220026Tue, 15 Nov 2016 22:00 ESTA Lie Algebraic and Numerical Investigation of the Black-Scholes Equation with Heston Volatility Modelhttp://projecteuclid.org/euclid.jglta/1479265225<strong>J Merger</strong>, <strong>A Borzi</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number S2, 7 pages.</p><p><strong>Abstract:</strong><br/>
This work deals with an extension of the Black-Scholes model for rating options with the Heston volatility model.
A Lie-algebraic analysis of this equation is applied to reduce its order and compute some of its solutions. As a result
of this method, a five-parameter family of solutions is obtained. Though, these solutions do not match the terminal and
boundary conditions, they can be used for the validation of numerical schemes.
</p>projecteuclid.org/euclid.jglta/1479265225_20161115220026Tue, 15 Nov 2016 22:00 ESTReal Multiplication Revisitedhttp://projecteuclid.org/euclid.jglta/1479265226<strong>IV Nikolaev</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number S2, 5 pages.</p><p><strong>Abstract:</strong><br/>
It is proved that the Hilbert class field of a real quadratic field $Q(\sqrt{D})$ modulo a power $m$ of the conductor $f$ is
generated by the Fourier coefficients of the Hecke eigenform for a congruence subgroup of level $fD$.
</p>projecteuclid.org/euclid.jglta/1479265226_20161115220026Tue, 15 Nov 2016 22:00 ESTMathematical Aspects of Sikidyhttp://projecteuclid.org/euclid.jglta/1479265227<strong>FM Anona</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number S2, 3 pages.</p><p><strong>Abstract:</strong><br/>
It emphasizes the mathematical aspects of the formation of sikidy. The sikidy as an art of divination is transmitted
by oral tradition, the knowledge of these mathematical relationships allows for a more consistent language of sikidy. In
particular, one can calculate systematically all ”into sikidy” special tables of Sikidy used in the ”ody” (kind of talismans).
</p>projecteuclid.org/euclid.jglta/1479265227_20161115220026Tue, 15 Nov 2016 22:00 ESTTrying to Explicit Proofs of Some Veys Theorems in Linear Connectionshttp://projecteuclid.org/euclid.jglta/1479265228<strong>LS Lantonirina</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number S2, 4 pages.</p><p><strong>Abstract:</strong><br/>
Let Χ a diferentiable paracompact manifold. Under the hypothesis of a linear connection r with free torsion Τ on
Χ, we are going to give more explicit the proofs done by Vey for constructing a Riemannian structure. We proposed
three ways to reach our object. First, we give a sufficient and necessary condition on all of holonomy groups of the
connection ∇ to obtain Riemannian structure. Next, in the analytic case of $Χ$, the existence of a quadratic positive
definite form g on the tangent bundle ΤΧ such that it was invariant in the infinitesimal sense by the linear operators
∇$^k$R, where R is the curvature of ∇, shows that the connection ∇ comes from a Riemannian structure. At last, for a
simply connected manifold Χ, we give some conditions on the linear envelope of the curvature R to have a Riemannian
structure.
</p>projecteuclid.org/euclid.jglta/1479265228_20161115220026Tue, 15 Nov 2016 22:00 ESTHeat Conduction: Hyperbolic Self-similar Shock-waves in Solid Mediumhttp://projecteuclid.org/euclid.jglta/1479265229<strong>IF Barna</strong>, <strong>R Kersner</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number S2, 4 pages.</p><p><strong>Abstract:</strong><br/>
Analytic solutions for cylindrical thermal waves in solid medium are given based on the nonlinear hyperbolic
system of heat flux relaxation and energy conservation equations. The Fourier-Cattaneo phenomenological law
is generalized where the relaxation time and heat propagation coefficient have a general power law temperature
dependence. From such laws one cannot form a second order parabolic or telegraph-type equation.We consider the
original non-linear hyperbolic system itself with the self-similar Ansatz for the temperature distribution and for the heat
flux. As results continuous.
</p>projecteuclid.org/euclid.jglta/1479265229_20161115220026Tue, 15 Nov 2016 22:00 ESTThe ABCs of the Mathematical Infinitology. Principles of the Modern Theory and Practice of Scientific-and-Mathematical Infinitologyhttp://projecteuclid.org/euclid.jglta/1479265230<strong>EV Karpushkin </strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number S2, 14 pages.</p><p><strong>Abstract:</strong><br/>
The modern Science has now a lot of its branches and meanders, where are working the numerous specialists
and outstanding scientists everywhere in the whole world. The theme of this article is devoted to mathematics in
general and to such a new subsidiary science as the Cartesian infinitology (± ∞: x y and x y z) in a whole.
The young and adult modern people of our time, among them, in first turn, are such ones as the usual citizens,
students or schoolchildren, have a very poor imagination about those achievements and successes that made by our
scientists in the different parts and divisions of many fundamental sciences, especially in mathematics. This article is a
short description of the numerous ideas of a new science that is named by its inventor as the mathematical infinitology.
The infinity as the scientific category is a very complicated conception and the difficult theme for professional
discussing of its properties and features even by the academicians and the Nobelists as well. In spite of all problems,
the author have found his own road to this Science and worked out independently, even not being a mathematician
at all, the universal, from his point of view, and unusual theories and scientific methods, which helped him to find
and name It as the mathematical infinitology, that may be now studied in rectangular system of Cartesian or other
coordinates, in orthogonal ones, for example, as easy and practically as we study the organic chemistry or Chinese
language at the middle school or in the University.
The mathematical infinitology, as a separate or independent science, has been never existed in the mathematics
from the ancient times up to the 90-th years of the XX-th century. All outstanding mathematicians of the past times
were able only approximately to image to themselves and explain to their colleagues and pupils in addition, what is an
infinity indeed: the scientific abstraction or the natural mathematical science that can be not only tested by one’s tooth
or touched by hands, but study and investigate it in schools or the Institutions of higher learning too.
The article author without no one imagination, what it is indeed. Very long time working hours spent by the inventor
with this mathematical toy or the simplest logical entertainment helped him to penetrate into the mysteries of this
usual intellectual mathematical object and see in it the fantastic perspectives and possibilities as for science as for
himself in further studying and it investigating. In a result of the own purposefulness and interests to the re-invented
mathematical idea of the famous American mathematician S.M.Ulam, the new science was born in the World, and
after long time experiments, it was named as the mathematical or Cartesian infinitology (±∞ : x y and x y z).
</p>projecteuclid.org/euclid.jglta/1479265230_20161115220026Tue, 15 Nov 2016 22:00 ESTProperties of Nilpotent Orbit Complexificationhttp://projecteuclid.org/euclid.jglta/1479265231<strong>Peter Crooks</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number S2, pages.</p><p><strong>Abstract:</strong><br/>
We consider aspects of the relationship between nilpotent orbits in a semisimple real Lie algebra $\mathfrak{g}$ and those in
its complexification $\mathfrak{g}_{\mathbb{C}}$. In particular, we prove that two distinct real nilpotent orbits lying in the same complex orbit are
incomparable in the closure order. Secondly, we characterize those $\mathfrak{g}$ having non-empty intersections with all nilpotent
orbits in $\mathfrak{g}_{\mathbb{C}}$. Finally, for $\mathfrak{g}$ quasi-split, we characterize those complex nilpotent orbits containing real ones.
</p>projecteuclid.org/euclid.jglta/1479265231_20161115220026Tue, 15 Nov 2016 22:00 ESTLie Group Methods for Eigenvalue Functionhttp://projecteuclid.org/euclid.jglta/1486090819<strong>HA Nazarkandi</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number 1, 4 pages.</p><p><strong>Abstract:</strong><br/>
By considering a C∞ structure on the ordered non-increasing of elements of Rn, we
show that it is a differentiable manifold. By using of Lie groups, we show that
eigenvalue function is a submersion. This fact is used to prove some results.
These results is applied to prove a few facts about spectral manifolds and
spectral functions. Orthogonal matrices act on the real symmetric matrices as a
Lie transformation group. This fact, also, is used to prove the results.
</p>projecteuclid.org/euclid.jglta/1486090819_20170202220026Thu, 02 Feb 2017 22:00 ESTClassification of Canonical Bases for (n−1)−dimensional Subspaces of n−
Dimensional Vector Spacehttp://projecteuclid.org/euclid.jglta/1486090820<strong>Uladzimir Shtukar</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number 1, 4 pages.</p><p><strong>Abstract:</strong><br/>
Canonical bases for (n-1)-dimensional subspaces of n-dimensional vector space are
introduced and classified in the article. This result is very prospective to
utilize canonical bases at all applications. For example, maximal subalgebras of
Lie algebras can be found using them.
</p>projecteuclid.org/euclid.jglta/1486090820_20170202220026Thu, 02 Feb 2017 22:00 ESTHilbert-substructure of Real Measurable Spaces on Reductive Groups, I; Basic
Theoryhttp://projecteuclid.org/euclid.jglta/1486090821<strong>OO Oyadare</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number 1, 4 pages.</p><p><strong>Abstract:</strong><br/>
This paper reconsiders the age-long problem of normed linear spaces which do not
admit inner product and shows that, for some subspaces, Fn(G), of real
Lp(G)−spaces (when G is a reductive group in the Harish-Chandra class and p=2n),
the situation may be rectified, via an outlook which generalizes the fine
structure of the Hilbert space, L2(G). This success opens the door for harmonic
analysis of unitary representations, G→End(Fn(G)), of G on the
Hilbert-substructure Fn(G), which has hitherto been considered impossible.
</p>projecteuclid.org/euclid.jglta/1486090821_20170202220026Thu, 02 Feb 2017 22:00 ESTCanonical Bases for Subspaces of a Vector Space, and 5-Dimensional Subalgebras of
Lie Algebra of Lorentz Grouphttp://projecteuclid.org/euclid.jglta/1486090822<strong>Uladzimir Shtukar</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number 1, 6 pages.</p><p><strong>Abstract:</strong><br/>
Canonical bases for subspaces of a vector space are introduced as a new effective
method to analyze subalgebras of Lie algebras. This method generalizes well
known Gauss-Jordan elimination method.
</p>projecteuclid.org/euclid.jglta/1486090822_20170202220026Thu, 02 Feb 2017 22:00 ESTStructure Theory of Rack-Bialgebrashttp://projecteuclid.org/euclid.jglta/1486090823<strong>C Alexandre</strong>, <strong>M Bordemann</strong>, <strong>S Rivière</strong>, <strong>F Wagemann</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number 1, 20 pages.</p><p><strong>Abstract:</strong><br/>
In this paper we focus on a certain self-distributive multiplication on
coalgebras, which leads to so-called rack bialgebra. Inspired by semi-group
theory (adapting the Suschkewitsch theorem), we do some structure theory for
rack bialgebras and cocommutative Hopf dialgebras. We also construct canonical
rack bialgebras (some kind of enveloping algebras) for any Leibniz algebra and
compare to the existing constructions. We are motivated by a differential
geometric procedure which we call the Serre functor: To a pointed differentible
manifold with multiplication is associated its distribution space supported in
the chosen point. For Lie groups, it is wellknown that this leads to the
universal enveloping algebra of the Lie algebra. For Lie racks, we get
rack-bialgebras, for Lie digroups, we obtain cocommutative Hopf dialgebras.
</p>projecteuclid.org/euclid.jglta/1486090823_20170202220026Thu, 02 Feb 2017 22:00 ESTClassification of Canonical Bases for (n-2)-Dimensional Subspaces of
n-Dimensional Vector Spacehttp://projecteuclid.org/euclid.jglta/1486090824<strong>U Shtukar</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number 1, 8 pages.</p><p><strong>Abstract:</strong><br/>
Famous K. Gauss introduced reduced row echelon forms for matrices approximately
200 years ago to solve systems of linear equations but the number of them and
their structure has been unknown until 2016 when it was determined at first in
the previous article given up to (n−1)×n matrices. The similar method is applied
to find reduced row echelon forms for (n−2)×n matrices in this article, and all
canonical bases for (n−2)-dimensional subspaces of -dimensional vector space are
found also.
</p>projecteuclid.org/euclid.jglta/1486090824_20170202220026Thu, 02 Feb 2017 22:00 ESTCentralizers of Commuting Elements in Compact Lie Groupshttp://projecteuclid.org/euclid.jglta/1486090825<strong>Kris A Nairn</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number 1, 5 pages.</p><p><strong>Abstract:</strong><br/>
The moduli space for a flat G-bundle over the two-torus is completely determined
by its holonomy representation. When G is compact, connected, and simply
connected, we show that the moduli space is homeomorphic to a product of two
tori mod the action of the Weyl group, or equivalently to the conjugacy classes
of commuting pairs of elements in G. Since the component group for a non-simply
connected group is given by some finite dimensional subgroup in the centralizer
of an n-tuple, we use diagram automorphisms of the extended Dynkin diagram to
prove properties of centralizers of pairs of elements in G.
</p>projecteuclid.org/euclid.jglta/1486090825_20170202220026Thu, 02 Feb 2017 22:00 ESTStructures of Not-finitely Graded Lie Superalgebrashttp://projecteuclid.org/euclid.jglta/1486090826<strong>Juanjuan Li</strong>, <strong>Guangzhe Fan</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number 1, 5 pages.</p><p><strong>Abstract:</strong><br/>
This paper is devoted to investigating the structure theory of a class of
not-finitely graded Lie superalgebras related to generalized super-Virasoro
algebras. In particular, we completely determine the derivation algebras, the
automorphism groups and the second cohomology groups of these Lie
superalgebras.
</p>projecteuclid.org/euclid.jglta/1486090826_20170202220026Thu, 02 Feb 2017 22:00 ESTThe Hypergeometrical Universe: Cosmogenesis, Cosmology and Standard Modelhttp://projecteuclid.org/euclid.jglta/1486090827<strong>MA Pereira</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number 1, 26 pages.</p><p><strong>Abstract:</strong><br/>
This paper presents a simple and purely geometrical Grand Unification Theory.
Quantum Gravity, Electrostatic and Magnetic interactions are shown in a unified
framework. Newton’s Gravitational Law, Gauss’ Electrostatics Law and
Biot-Savart’s Electromagnetism Law are derived from first principles.
Gravitational Lensing, Mercury Perihelion Precession are replicated within the
theory. Unification symmetry is defined for all the existing forces. This
alternative model does not require Strong and Electroweak forces. A 4D
Shock-Wave Hyperspherical topology is proposed for the Universe which together
with a Quantum Lagrangian Principle and a Dilator based model for matter result
in a quantized stepwise expansion for the whole Universe along a radial
direction within a 4D spatial manifold. The Hypergeometrical Standard Model for
matter, Universe Topology, Simple Cosmogenesis and a new Law of Gravitation are
presented. Type 1A Supernova Survey HU results is provided. A New de-Broglie
Force is proposed.
</p>projecteuclid.org/euclid.jglta/1486090827_20170202220026Thu, 02 Feb 2017 22:00 ESTReduction over Coset Spaces and Residual Gauge Symmetryhttp://projecteuclid.org/euclid.jglta/1486090828<strong>S Davis</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number 1, 8 pages.</p><p><strong>Abstract:</strong><br/>
The reduction of higher-dimensional theories over a coset space S/R is known to
yield a residual gauge symmetry related to the number of R-singlets in the
decomposition of S with respect to R. It is verified that this invariance is
identical to that found by requiring that there is a subgroup of the isometry
group with an action on the connection form that yields a transformation rule
defined only on the base space. The Lagrangian formulation of the projection of
the frame of global vector fields from S7 to the Lie group submanifold S3× S3 is
considered. The structure of an octonionic Chern-Simons gauge theory is
described.
</p>projecteuclid.org/euclid.jglta/1486090828_20170202220026Thu, 02 Feb 2017 22:00 ESTHow to Prove the Riemann Hypothesishttp://projecteuclid.org/euclid.jglta/1486090829<strong>Fayez Fok Al Adeh</strong>. <p><strong>Source: </strong>Journal of Generalized Lie Theory and Applications, Volume 10, Number 1, 5 pages.</p><p><strong>Abstract:</strong><br/>
The aim of this paper is to prove the celebrated Riemann Hypothesis. I have already discovered a simple proof of the Riemann Hypothesis. The hypothesis states that the nontrivial zeros of the Riemann zeta function have real part equal to 0.5. I assume that any such zero is s=a+bi. I use integral calculus in the first part of the proof. In the second part I employ variational calculus. Through equations (50) to (59) I consider (a) as a fixed exponent, and verify that a=0.5. From equation (60) onward I view (a) as a parameter (a <0.5) and arrive at a contradiction. At the end of the proof (from equation (73)) and through the assumption that (a) is a parameter, I verify again that a=0.5.
</p>projecteuclid.org/euclid.jglta/1486090829_20170202220026Thu, 02 Feb 2017 22:00 EST