A non-abelian Hom-Leibniz tensor product and applications

TL;DR

This paper introduces a non-abelian Hom-Leibniz tensor product, explores its properties, and applies it to universal central extensions and Hochschild homology in Hom-algebra structures.

Contribution

It defines a new tensor product for Hom-Leibniz algebras and demonstrates its applications to central extensions and Hochschild homology.

Findings

Established properties of the non-abelian Hom-Leibniz tensor product

Applied the tensor product to describe universal central extensions

Connected the tensor product to Hochschild homology of Hom-associative algebras

Abstract

The notion of non-abelian Hom-Leibniz tensor product is introduced and some properties are established. This tensor product is used in the description of the universal ($\alpha$-)central extensions of Hom-Leibniz algebras. We also give its application to the Hochschild homology of Hom-associative algebras.