Universal Algebra of a Hom-Lie Algebra and group-like elements

TL;DR

This paper develops a universal enveloping algebra for Hom-Lie algebras, endowing it with a Hom-Hopf algebra structure, and explores group-like elements as Hom-groups integrating the original algebra.

Contribution

It introduces the construction of a universal enveloping algebra for Hom-Lie algebras with a Hom-Hopf algebra structure and studies their group-like elements.

Findings

Established the Hom-Hopf algebra structure on the universal enveloping algebra.

Identified group-like elements as Hom-groups integrating the Hom-Lie algebra.

Provided a framework connecting Hom-Lie algebras with Hom-group structures.

Abstract

We construct the universal enveloping algebra of a Hom-Lie algebra and endow it with a Hom-Hopf algebra structure. We discuss group-like elements that we see as a Hom-group integrating the initial Hom-Lie algebra.