On the univeral \alpha-central extensions of the semi-direct product of Hom-Leibniz algebras

Abstract

We introduce Hom-actions, semi-direct product and establish the equivalence between split extensions and the semi-direct product extension of Hom-Leibniz algebras. We analyze the functorial properties of the universal ({\alpha})-central extensions of ({\alpha})-perfect Hom-Leibniz algebras. We establish under what conditions an automorphism or a derivation can be lifted in an {\alpha}-cover and we analyze the universal {\alpha}-central extension of the semi-direct product of two {\alpha}-perfect Hom-Leibniz algebras.