On Hom-Leibniz and Hom-Lie-Yamaguti Superalgebras

Abstract

In this paper some characterizations of Hom-Leibniz superalgebras are given and some of their basic properties are found. These properties can be seen as a generalization of corresponding well-known properties of Hom-Leibniz algebras. Considering the Hom-Akivis superalgebra associated to a given Hom-Leibniz superalgebra, it is observed that the Hom-super Akivis identity leads to an additional property of Hom-Leibniz superalgebras, which in turn gives a necessary and sufficient condition for Hom-super Lie admissibility of Hom-Leibniz superalgebras. We show also that every (left) Hom-Leibniz superalgebra has a natural Hom-Lie-Yamaguti superalgebra structure.

References in corpus (6)

• On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
• Deformations of Hom-Alternative and Hom-Malcev algebras
• A twisted generalization of Lie-Yamaguti algebras
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Cited by in corpus (2)

• On split regular BiHom-Leibniz superalgebras
• Representations and deformations of Hom-Lie-Yamaguti superalgebras