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 admis- sibility of Hom-Leibniz superalgebras. We also show that every (left) Hom-Leibniz superalgebra has a natural super Hom-Lie-Yamaguti structure.