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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 275250, 8 pages
http://dx.doi.org/10.1155/2013/275250
Research Article

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

Department of Mathematics, Tongji University, Shanghai 200092, China

Received 21 March 2013; Accepted 19 June 2013

Academic Editor: Shi Weichen

Copyright © 2013 Xiuxian Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. 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. View at Zentralblatt MATH · View at MathSciNet
  2. R. M. Santilli, “Invariant Lie-admissible formulation of quantum deformations,” Foundations of Physics, vol. 27, no. 8, pp. 1159–1177, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  3. D. S. Sourlas and G. T. Tsagas, Mathematical Foundations of the Lie-Santilli Theory, “Naukova Dumka”, Kiev, Ukraine, 1993. View at MathSciNet
  4. J. T. Hartwig, D. Larsson, and S. D. Silvestrov, “Deformations of Lie algebras using σ-derivations,” Journal of Algebra, vol. 295, no. 2, pp. 314–361, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  5. D. Larsson and S. D. Silvestrov, “Quasi-Lie algebras,” Contemporary Mathematics, vol. 391, pp. 241–248, 2005.
  6. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. N. Hu, “q-Witt algebras, q-Lie algebras, q-holomorph structure and representations,” Algebra Colloquium, vol. 6, no. 1, pp. 51–70, 1999. View at MathSciNet
  8. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. A. Makhlouf and S. D. Silvestrov, “Hom-algebra structures,” Journal of Generalized Lie Theory and Applications, vol. 2, no. 2, pp. 51–64, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer, New York, NY, USA, 1972. View at MathSciNet
  12. N. Jacobson, Lie Algebras, Dover, New York, NY, USA, 1962. View at MathSciNet
  13. Y. Sheng, “Representations of hom-Lie algebras,” Algebras and Representation Theory, vol. 15, no. 6, pp. 1081–1098, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  14. D. Yau, “Hom-algebras and homology,” Journal of Lie Theory, vol. 19, no. 2, pp. 409–421, 2009. View at Zentralblatt MATH · View at MathSciNet
  15. D. Yau, “The Hom-Yang-Baxter equation and Hom-Lie algebras,” Journal of Mathematical Physics, vol. 52, no. 5, 2011. View at Publisher · View at Google Scholar · View at MathSciNet