Enveloping algebras of color hom-Lie algebras

TL;DR

This paper develops the theory of universal enveloping algebras for color hom-Lie algebras, extending classical results like the Poincaré-Birkhoff-Witt theorem to this new algebraic setting.

Contribution

It introduces a construction for the universal enveloping algebra of involutive color hom-Lie algebras and generalizes the PBW theorem to this context.

Findings

Constructed the free involutive hom-associative color algebra on a hom-module.

Established the universal enveloping algebra for involutive color hom-Lie algebras.

Extended the PBW theorem to involutive color hom-Lie algebras.

Abstract

In this paper the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free involutive hom-associative color algebra on a hom-module is described and applied to obtain the universal enveloping algebra of an involutive hom-Lie color algebra. Finally, the construction is applied to obtain the well-known Poincar{\'e}-Birkhoff-Witt theorem for Lie algebras to the enveloping algebra of an involutive color hom-Lie algebra.