Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON HOM-LIE TRIPLE SYSTEMS AND INVOLUTIONS OF HOM-LIE ALGEBRAS

  • Yara, Hamdiatou (Department of Mathematics, Thomas Sankara University) ;
  • Zoungrana, Patricia L. (Department of Mathematics, Thomas Sankara University)
  • Received : 2022.03.21
  • Accepted : 2022.06.09
  • Published : 2022.06.30
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Abstract

In this paper we mainly establish a relationship between involutions of multiplicative Hom-Lie algebras and Hom-Lie triple systems. We show that the -1-eigenspace of any involution on any multiplicative Hom-Lie algebra becomes a Hom-Lie triple system and we construct some examples of Hom-Lie triple systems using some involutions of some classical Hom-Lie algebras.

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References

  1. A. Baklouti, Quadratic Hom-Lie triple systems, J. Geom. Phys. 121 (2017), 166-175. https://doi.org/10.1016/j.geomphys.2017.06.013
  2. S. Benayadi and A. Makhlouf, Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms, J. Geom. Phys. 76 (2014), 38-60. https://doi.org/10.1016/j.geomphys.2013.10.010
  3. E. Cartan, Oeuvres completes, Part 1, vol. 2, nos. 101, 138, Paris, Gauthier-Villars, 1952.
  4. J. T. Hartwig, D. Larsson and S.D. Silvestrov, Deformations of Lie algebras unsing σ-derivations, J. Algebra. 295 (2006), 314-361. https://doi.org/10.1016/j.jalgebra.2005.07.036
  5. T. L. Hodge, Lie triple systems, restricted Lie triple systems and algebraic groups, J. Algebra. 244 (2001), 533-580. https://doi.org/10.1006/jabr.2001.8890
  6. N. Jacobson, Lie and Jordan triple systems, Amer. J. Math. 71 (1949), 149-170. https://doi.org/10.2307/2372102
  7. N. Jacobson, General representation theory of Jordan algebras, Trans. Amer. Math. Soc. 70 (1951), 509-548. https://doi.org/10.1090/S0002-9947-1951-0041118-9
  8. W. G. Lister, A structure theory for Lie triple systems, Trans. Amer. Math. Soc. 72 (1952), 217-242. https://doi.org/10.1090/S0002-9947-1952-0045702-9
  9. D. Yau, On n-ary Hom-Nambu and Hom-Nambu-Lie algebras, J. Geom. Phys. 62 (2012), 506-522. https://doi.org/10.1016/j.geomphys.2011.11.006
  10. D. Yau, Hom-algebras and homology, J. Lie Theory. 19 (2009), 409-421.
  11. J. Zhou, L. Chen and Y. Ma, Generalized derivations of Lie triple systems, Open Math. 14 (2016), 260-271. https://doi.org/10.1515/math-2016-0024