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

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.

On the capablility of Hom-Lie algebras

“…Any Lie algebra included into HomLie satisfies the α-identity condition and more examples can be found in [10,11]. Proposition 3.10.…”