On the Universal $$\alpha $$ α -Central Extension of the Semi-direct Product of Hom-Leibniz Algebras

Abstract

We introduce Hom-actions, semidirect 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.