A non-abelian tensor product of Hom-Lie algebras

TL;DR

This paper introduces a non-abelian tensor product for Hom-Lie algebras, exploring its properties and applications in describing universal central extensions and relating different homologies.

Contribution

It constructs a new tensor product for Hom-Lie algebras and applies it to universal extensions and homology relations, advancing the algebraic theory.

Findings

Defined the non-abelian tensor product for Hom-Lie algebras

Connected tensor product with universal central extensions

Linked cyclic and Milnor cyclic homologies under certain conditions

Abstract

Non-abelian tensor product of Hom-Lie algebras is constructed and studied. This tensor product is used to describe universal ($\alpha$-)central extensions of Hom-Lie algebras and to establish a relation between cyclic and Milnor cyclic homologies of Hom-associative algebras satisfying certain additional condition.