Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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HOM-LIE-YAMAGUTI SUPERALGEBRAS

  • Gaparayi, Donatien (Ecole Normale Superieure (E.N.S)) ;
  • Attan, Sylvain (Departement de Mathematiques Universite d'Abomey-Calavi) ;
  • Issa, A. Nourou (Departement de Mathematiques Universite d'Abomey-Calavi)
  • Received : 2018.07.02
  • Accepted : 2019.03.18
  • Published : 2019.03.30
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Abstract

(Multiplicative) Hom-Lie-Yamaguti superalgebras are defined as a ${\mathbb{Z}}_2$-graded generalization of Hom-Lie Yamaguti algebras and also as a twisted generalization of Lie-Yamaguti superalgebras. Hom-Lie-Yamaguti superalgebras generalize also Hom-Lie supertriple systems (and subsequently ternary multiplicative Hom-Nambu superalgebras) and Hom-Lie superalgebras in the same way as Lie-Yamaguti superalgebras generalize Lie supertriple systems and Lie superalgebras. Hom-Lie-Yamaguti superalgebras are obtained from Lie-Yamaguti superalgebras by twisting along superalgebra even endomorphisms. We show that the category of (multiplicative) Hom-Lie-Yamaguti superalgebras is closed under twisting by self-morphisms. Constructions of some examples of Hom-Lie-Yamaguti superalgebras are given. The notion of an nth derived (binary) Hom-superalgebras is extended to the one of an nth derived binary-ternary Hom-superalgebras and it is shown that the category of Hom-Lie-Yamaguti superalgebras is closed under the process of taking nth derived Hom-superalgebras.

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References

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