On some properties preserved by the non-abelian tensor product of Hom-Lie algebras

TL;DR

This paper investigates how the non-abelian tensor product of Hom-Lie algebras preserves algebraic properties like solvability and nilpotency, and explores its compatibility with universal central extensions.

Contribution

It provides new insights into the structural properties preserved by the non-abelian tensor product in Hom-Lie algebras and its relation to universal central extensions.

Findings

Preservation of products and quotients in Hom-Lie algebras

Compatibility with universal central extensions

Conditions under which solvability and nilpotency are preserved

Abstract

We study some properties of the non-abelian tensor product of Hom-Lie algebras concerning the preservation of products and quotients, solvability and nilpotency, and describe compatibility with the universal central extensions of perfect Hom-Lie algebras.