Abstract and Applied Analysis

A Realization of Hom-Lie Algebras by Iso-Deformed Commutator Bracket

Xiuxian Li

Full-text: Open access

Abstract

We construct classical Iso-Lie and Iso-Hom-Lie algebras in g l ( V ) by twisted commutator bracket through Iso-deformation. We prove that they are simple. Their Iso-automorphisms and isotopies are also presented.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 275250, 8 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393444219

Digital Object Identifier
doi:10.1155/2013/275250

Mathematical Reviews number (MathSciNet)
MR3089537

Zentralblatt MATH identifier
1359.17004

Citation

Li, Xiuxian. A Realization of Hom-Lie Algebras by Iso-Deformed Commutator Bracket. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 275250, 8 pages. doi:10.1155/2013/275250. https://projecteuclid.org/euclid.aaa/1393444219


Export citation

References

  • R. M. Santilli, “Addendum to: `On a possible Lie-admissible covering of the Galilei relativity in Newtonian mechanics for nonconservative and Galilei form-noninvariant systems',” Hadronic Journal, vol. 1, no. 4, pp. 1279–1342, 1978.
  • R. M. Santilli, “Invariant Lie-admissible formulation of quantum deformations,” Foundations of Physics, vol. 27, no. 8, pp. 1159–1177, 1997.
  • D. S. Sourlas and G. T. Tsagas, Mathematical Foundations of the Lie-Santilli Theory, “Naukova Dumka”, Kiev, Ukraine, 1993.
  • J. T. Hartwig, D. Larsson, and S. D. Silvestrov, “Deformations of Lie algebras using $\sigma $-derivations,” Journal of Algebra, vol. 295, no. 2, pp. 314–361, 2006.
  • D. Larsson and S. D. Silvestrov, “Quasi-Lie algebras,” Contemporary Mathematics, vol. 391, pp. 241–248, 2005.
  • D. Larsson and S. D. Silvestrov, “Quasi-hom-Lie algebras, central extensions and 2-cocycle-like identities,” Journal of Algebra, vol. 288, no. 2, pp. 321–344, 2005.
  • N. Hu, “$q$-Witt algebras, $q$-Lie algebras, $q$-holomorph structure and representations,” Algebra Colloquium, vol. 6, no. 1, pp. 51–70, 1999.
  • Q. Jin and X. Li, “Hom-Lie algebra structures on semi-simple Lie algebras,” Journal of Algebra, vol. 319, no. 4, pp. 1398–1408, 2008.
  • D. Yau, “The Hom-Yang-Baxter equation, Hom-Lie algebras, and quasi-triangular bialgebras,” Journal of Physics A, vol. 42, no. 16, pp. 165–202, 2009.
  • A. Makhlouf and S. D. Silvestrov, “Hom-algebra structures,” Journal of Generalized Lie Theory and Applications, vol. 2, no. 2, pp. 51–64, 2008.
  • J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer, New York, NY, USA, 1972.
  • N. Jacobson, Lie Algebras, Dover, New York, NY, USA, 1962.
  • Y. Sheng, “Representations of hom-Lie algebras,” Algebras and Representation Theory, vol. 15, no. 6, pp. 1081–1098, 2012.
  • D. Yau, “Hom-algebras and homology,” Journal of Lie Theory, vol. 19, no. 2, pp. 409–421, 2009.
  • D. Yau, “The Hom-Yang-Baxter equation and Hom-Lie algebras,” Journal of Mathematical Physics, vol. 52, no. 5, 2011.