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

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Published: Mar 30, 2019
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).
Mathematics Subject Classification:
17A30, 17A32, 17D99

Main Article Content

Donatien Gaparayi
Ecole Normale Sup erieure (E.N.S) BP 6983 Bujumbura, Burundi
Sylvain Attan
Département de Mathématiques, Université d'Abomey-calavi 01 BP 4521, Cotonou 01, Bénin.
A. Nourou Issa
Département de Mathématiques, Université d'Abomey-calavi 01 BP 4521, Cotonou 01, Bénin.

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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Donatien Gaparayi

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