Non-abelian Tensor Product Of Leibniz Superalgebras And Hom-Leibniz Superalgebras

This article gives the definition of Leibniz action,semi-direct product and crossed module of Leibniz superalgebras.Then we present homology and some results of low dimensional homology of Leibniz superalgebras.Next,non-abelian tensor product of Leibniz superalgebras is constructed and studied.We get some important propositions.Moreover,we generalise these results of Leibniz superalgeras to Hom-Leibniz superalgebras.We introduce Hom-Leibniz action,semi-direct product,crossed module and non-abelian tensor product of Hom-Leibniz superalgebras.Then we get some important results.This article enriches the knowledge of Leibniz superalgebras and Hom-Leibniz superalgebras,plays an important role in studying non-abelian tensor product of all kinds of algebras and promotes the development of Leibniz algebras.