Korean J. Math.  Vol 27, No 1 (2019)  pp.175-192
DOI: https://doi.org/10.11568/kjm.2019.27.1.175

Hom-Lie-Yamaguti superalgebras

Donatien Gaparayi, Sylvain Attan, A. Nourou Issa

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.

Keywords


Lie-Yamaguti superalgebra (i.e.generalized Lie supertriple system, Lie superalgebra), Hom-Lie-Yamaguti superalgebra (i.e.generalized Hom-Lie supertriple system, Hom-Lie superalgebra).

Subject classification

17A30, 17A32, 17D99

Sponsor(s)

Donatien Gaparayi

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