On the homotopy Lie algebra of an arrangement
Graham Denham and Alexander I. Suciu
Source: Michigan Math. J. Volume 54, Issue 2 (2006), 319-340.
Primary Subjects: 16E05, 52C35
Secondary Subjects: 16S37, 55P62
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05140635
References
L. Avramov, Small homomorphisms of local rings, J. Algebra 50 (1978), 400--453.
Mathematical Reviews (MathSciNet):
MR485906
Digital Object Identifier: doi:10.1016/0021-8693(78)90163-1
------, Golod homomorphisms, Algebra, algebraic topology and their interactions (Stockholm, 1983), Lecture Notes in Math., 1183, pp. 59--78, Springer-Verlag, Berlin, 1986.
Mathematical Reviews (MathSciNet):
MR846439
Zentralblatt MATH:
0589.13004
Digital Object Identifier: doi:10.1007/BFb0075450
------, Infinite free resolutions, Six lectures on commutative algebra (Bellaterra, 1996), Progr. Math., 166, pp. 1--118, Birkhäuser, Basel, 1998.
Mathematical Reviews (MathSciNet):
MR1648664
Zentralblatt MATH:
0934.13008
A. Björner and G. Ziegler, Broken circuit complexes: Factorizations and generalizations, J. Combin. Theory Ser. B 51 (1991), 96--126.
Mathematical Reviews (MathSciNet):
MR1088629
Digital Object Identifier: doi:10.1016/0095-8956(91)90008-8
D. C. Cohen, F. R. Cohen, and M. Xicoténcatl, Lie algebras associated to fiber-type arrangements, Internat. Math. Res. Notices 29 (2003), 1591--1621.
Mathematical Reviews (MathSciNet):
MR1979686
Digital Object Identifier: doi:10.1155/S1073792803208102
G. Denham and S. Yuzvinsky, Annihilators of Orlik--Solomon relations, Adv. in Appl. Math. 28 (2002), 231--249.
Mathematical Reviews (MathSciNet):
MR1888846
Digital Object Identifier: doi:10.1006/aama.2001.0779
A. Dimca and S. Papadima, Hypersurface complements, Milnor fibers and higher homotopy groups of arrangments, Ann. of Math. (2) 158 (2003), 473--507.
Mathematical Reviews (MathSciNet):
MR2018927
Project Euclid: euclid.annm/1069786252
D. Eisenbud, S. Popescu, and S. Yuzvinsky, Hyperplane arrangement cohomology and monomials in the exterior algebra, Trans. Amer. Math. Soc. 355 (2003), 4365--4383.
Mathematical Reviews (MathSciNet):
MR1986506
Digital Object Identifier: doi:10.1090/S0002-9947-03-03292-6
M. Falk, The minimal model of the complement of an arrangement of hyperplanes, Trans. Amer. Math. Soc. 309 (1988), 543--556.
Mathematical Reviews (MathSciNet):
MR929668
Digital Object Identifier: doi:10.2307/2000924
JSTOR: links.jstor.org
------, Line-closed matroids, quadratic algebras, and formal arrangements, Adv. in Appl. Math. 28 (2002), 250--271.
Mathematical Reviews (MathSciNet):
MR1888847
Digital Object Identifier: doi:10.1006/aama.2001.0780
M. Falk and R. Randell, The lower central series of a fiber-type arrangement, Invent. Math. 82 (1985), 77--88.
Mathematical Reviews (MathSciNet):
MR808110
Digital Object Identifier: doi:10.1007/BF01394780
Y. Félix and J.-C. Thomas, On the ubiquity of the rational homotopy Lie algebra of a topological space, Bull. Soc. Math. Belg. Sér. A 38 (1986), 175--190.
Mathematical Reviews (MathSciNet):
MR885529
R. Fröberg, Koszul algebras, Advances in commutative ring theory (Fez, 1997), Lecture Notes in Pure and Appl. Math., 205, pp. 337--350, Dekker, New York, 1999.
Mathematical Reviews (MathSciNet):
MR1767430
R. Fröberg and C. Löfwall, Koszul homology and Lie algebras with application to generic forms and points, Homology Homotopy Appl. 4 (2002), 227--258.
Mathematical Reviews (MathSciNet):
MR1918511
Project Euclid: euclid.hha/1139852464
D. Grayson and M. Stillman, Macaulay 2: A software system for research in algebraic geometry; available at $\langle $http://www.math.uiuc.edu/Macaulay2$\rangle .$
M. Jambu and S. Papadima, A generalization of fiber-type arrangements and a new deformation method, Topology 37 (1998), 1135--1164.
Mathematical Reviews (MathSciNet):
MR1632975
Digital Object Identifier: doi:10.1016/S0040-9383(97)00092-X
------, Deformations of hypersolvable arrangements, Arrangements in Boston: A conference on hyperplane arrangements (1999), Topology Appl. 118 (2002), 103--111.
Mathematical Reviews (MathSciNet):
MR1877718
Digital Object Identifier: doi:10.1016/S0166-8641(01)00044-X
P. Jørgensen, Non-commutative Castelnuovo--Mumford regularity, Math. Proc. Cambridge Philos. Soc. 125 (1999), 203--221.
Mathematical Reviews (MathSciNet):
MR1643863
Digital Object Identifier: doi:10.1017/S0305004198002862
C. Löfwall, On the subalgebra generated by the one-dimensional elements in the Yoneda Ext-algebra, Algebra, algebraic topology and their interactions (Stockholm, 1983), Lecture Notes in Math., 1183, pp. 291--338, Springer-Verlag, Berlin, 1986.
Mathematical Reviews (MathSciNet):
MR846457
J. W. Milnor and J. C. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211--264.
Mathematical Reviews (MathSciNet):
MR174052
Digital Object Identifier: doi:10.2307/1970615
JSTOR: links.jstor.org
H. K. Nandi, Enumeration of non-isomorphic solutations of balanced incomplete block designs, Sankhy\B a 7 (1946), 305--312.
Mathematical Reviews (MathSciNet):
MR17247
P. Orlik and H. Terao, Arrangements of hyperplanes, Grundlehren Math. Wiss., 300, Springer-Verlag, Berlin, 1992.
Mathematical Reviews (MathSciNet):
MR1217488
Zentralblatt MATH:
0757.55001
S. Papadima and A. I. Suciu, Higher homotopy groups of complements of complex hyperplane arrangements, Adv. Math. 165 (2002), 71--100.
Mathematical Reviews (MathSciNet):
MR1880322
Digital Object Identifier: doi:10.1006/aima.2001.2023
------, Homotopy Lie algebras, lower central series, and the Koszul property, Geom. Topol. 8 (2004), 1079--1125.
Mathematical Reviews (MathSciNet):
MR2087079
Digital Object Identifier: doi:10.2140/gt.2004.8.1079
S. Papadima and S. Yuzvinsky, On rational $K[\pi ,1]$ spaces and Koszul algebras, J. Pure Appl. Algebra 144 (1999), 157--167.
Mathematical Reviews (MathSciNet):
MR1731434
Digital Object Identifier: doi:10.1016/S0022-4049(98)00058-9
D. Quillen, On the associated graded ring of a group ring, J. Algebra 10 (1968), 411--418.
Mathematical Reviews (MathSciNet):
MR231919
Digital Object Identifier: doi:10.1016/0021-8693(68)90069-0
V. V. Schechtman and A. N. Varchenko, Arrangements of hyperplanes and Lie algebra homology, Invent. Math. 106 (1991), 139--194.
Mathematical Reviews (MathSciNet):
MR1123378
Digital Object Identifier: doi:10.1007/BF01243909
H. K. Schenck and A. I. Suciu, Resonance, linear syzygies, Chen groups, and the Bernstein--Gelfand--Gelfand correspondence, Trans. Amer. Math. Soc. 358 (2006), 2269--2289.
Mathematical Reviews (MathSciNet):
MR2197444
Digital Object Identifier: doi:10.1090/S0002-9947-05-03853-5
D. W. Sharpe and P. Vámos, Injective modules, Cambridge Tracts Math. Math. Phys., 62, Cambridge Univ. Press, London, 1972.
Mathematical Reviews (MathSciNet):
MR360706
Zentralblatt MATH:
0245.13001
B. Shelton and S. Yuzvinsky, Koszul algebras from graphs and hyperplane arrangements, J. London Math. Soc. (2) 56 (1997), 477--490.
Mathematical Reviews (MathSciNet):
MR1610447
Digital Object Identifier: doi:10.1112/S0024610797005553
D. Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977), 269--331.
Mathematical Reviews (MathSciNet):
MR646078
Digital Object Identifier: doi:10.1007/BF02684341
S. Yuzvinsky, Small rational model of subspace complement, Trans. Amer. Math. Soc. 354 (2002), 1921--1945.
Mathematical Reviews (MathSciNet):
MR1881024
Digital Object Identifier: doi:10.1090/S0002-9947-02-02924-0
JSTOR: links.jstor.org
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