Characterization of a special case of hom-Lie superalgebra

Document Type : Original Article

Authors

Department of Mathematics, College of Sciences, Shiraz University, P.O. Box 71457-44776, Shiraz, Iran

Abstract

In this paper, we introduce the notion of sympathetic hom-Lie superalgebras. We prove some results on sympathetic multiplicative hom-Lie superalgebras with surjective α. In particular, we find some equivalence condition in which a sympathetic graded hom-ideal is direct factor of multiplicative hom-Lie superalgebra.

Keywords

References

  • 1. N. Aizawa, H. Sato, q-Deformation of the Virasoro algebra with central extension, Phys.
    Lett. B 256(2), (1991), 185-190. (Hiroshima Univ. preprint, HUPD-9012 (1990)).
  • 2. F. Ammar, A. Makhlouf, Hom-Lie superalgebras and hom-Lie admissible superalgebras,
    J. Algebra, 324(7), (2010), 1513-1528.
  • 3. F. Ammar, A. Makhlouf, S. Silvestrov, Ternary q-Virasoro-Witt hom-Nambu-Lie algebras, J. Phys. A: Math. Theor. 43(26), (2010), 265204.
  • 4. F. Ammar, A. Makhlouf, N. Saadaoui, Cohomology of hom-Lie superalgebras and qdeformed Witt superalgebra, Czech Math. J. 63(3), (2013), 721-761.
  • 5. F. Ammar, I. Ayadi, S. Mabrouk, A. Makhlouf, Quadratic color hom-Lie algebras, In:
    Siles Molina, M., El Kaoutit, L., Louzari, M., Ben Yakoub, L., Benslimane, M. (eds),
    Associative and Non-Associative Algebras and Applications. MAMAA 2018. Springer
    Proceedings in Mathematics and Statistics, 311. Springer, Cham., (2020), 287-312.
  • 6. A.Armakan, M. R. Farhangdoost, Geometric aspects of extensions of hom-Lie superalgebras, Int. J. Geom. Methods Mod. Phys. 14(06), (2017), 1750085.
  • 7. A. Armakan, M. R. Farhangdoost, S. Silvestrov, Non-degenerate Killing forms on homLie Superalgebras, arXiv:2010.01778 [math.RA] (2021).
  • 8. A. Armakan, A. Razavi, Complete hom-Lie superlgebras, Comm. Algebra. 48(2), (2020),
    651-662.
  • 9. A. Armakan, S. Silvestrov, Enveloping algebras of certain types of color hom-Lie algebras. In: Silvestrov, S., Malyarenko, A., Ran˘ci´c, M. (Eds.), Algebraic Structures and
    Applications, Springer Proceedings in Mathematics and Statistics, 317, Springer, Ch.
    10, (2020), 257-284.
  • 10. A. Armakan, S. Silvestrov, M. R. Farhangdoost, Enveloping algebras of color hom-Lie
    algebras, Turk. J. Math. 43(1), (2019), 316-339.
  • 11. A. Armakan, S. Silvestrov, M. R. Farhangdoost, Extensions of hom-Lie color algebras,
    Georgian Mathematical Journal 28(1), (2019), 15-27.
  • 12. A. Armakan, S. Silvestrov, Color hom-Lie algebras, color hom-Leibniz algebras and color
    omni-hom-Lie algebras, arXiv:2010.06160 [math.RA] (2020).
  • 13. Y. Cao, L. Chen, On split regular hom-Lie color algebras, Comm. Algebra, 40, (2012),
    575-592.
  • 14. J. H. Chun, J. S. Lee, On complete Lie superalgebras, Comm. Korean. Math. Soc. 11,
    (1996), 323-334.
  • 15. M. Goto, Faithful representations of Lie groups I, Math. Japon., 1, (1948), 1-13.
  • 16. B. Guan, L. Chen, B. Sun, On hom-Lie superalgebras, Adv. Appl. Clifford Algebras,
    29(16) (2019).
  • 17. J. T. Hartwig, D. Larsson, S. D. Silvestrov, Deformations of Lie algebras using σderivations, J. Algebra, 295(2), (2006), 314-361. (Preprint in Mathematical Sciences
    2003:32, LUTFMA-5036-2003, Centre for Mathematical Sciences, Department of Mathematics, Lund Institute of Technology, 52 (2003)).
  • 18. D. Larsson, S. D. Silvestrov, Quasi-Lie algebras, In: J. Fuchs, J. Mickelsson, G. Rozemnblioum, A. Stolin, A. Westerberg, Noncommutative Geometry and Representation Theory in Mathematical Physics, Contemp. Math. 391, Amer. Math. Soc., Providence, RI,
    (2005), 241-248. (Preprints in Mathematical Sciences 2004:30, LUTFMA-5049-2004, Centre for Mathematical Sciences, Department of Mathematics, Lund Institute of Technology,
    Lund University (2004)).
  • 19. D. Larsson, S. D. Silvestrov, Graded quasi-Lie algebras, Czechoslovak J. Phys., 55(11),
    (2005), 1473-1478.
  • 20. K. Q. Liu, Characterizations of the quantum Witt algebra, Lett. Math. Phys. 24(4),
    (1992), 257-265.
  • 21. Y. Liu, L. Chen, Y. Ma, Hom-Nijienhuis operators and T
    ∗-extensions of hom-Lie superalgebras, Linear Algebra Appl. 439(7), (2013), 2131-2144.
  • 22. A. Makhlouf, Paradigm of nonassociative Hom-algebras and Hom-superalgebras, in: J.
    Carmona Tapia, A. Morales Campoy, A. M. Peralta Pereira, M. I. Ramrez lvarez (Eds.),
    Proceedings of Jordan Structures in Algebra and Analysis Meeting, Publishing house:
    Circulo Rojo, (2009), 145177.
  • 23. A. Makhlouf, S. D. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl. 2 (2),
    (2008), 51-64. (Preprints in Mathematical Sciences 2006:10, LUTFMA-5074-2006, Centre
    for Mathematical Sciences, Department of Mathematics, Lund Institute of Technology,
    Lund University (2006)).
  • 24. M. Musson, Lie Superalgebras and Enveloping Algebras. Graduate Studies in Mathematics. 131(2), (2008), 95-108.
  • 25. M. Scheunert, The theory of Lie superalgebras. An introduction, Lecture Notes in Mathematics, 716, Springer-Verlag (1979).
  • 26. L. Yuan, Hom-Lie color algebra structures, Comm. Algebra, 40(2), (2012), 575-592.
    27. J. Zhou, L. Chen, Y. Ma, Generalized derivations of hom-Lie superalgebras, Acta Math.
    Sinica (Chin. Ser.) 58, (2014), 3737-3751.
Journal of Finsler Geometry and its Applications
Volume 3, Issue 1
July 2022
Pages 118-126

Files

Share

How to cite

Statistics