Algebras of quotients of Hom-Lie algebras

TL;DR

This paper introduces and studies the properties of algebras of quotients for Hom-Lie algebras, establishing conditions for their existence and exploring their relationship with associative algebras of derivations.

Contribution

It defines algebras of quotients for Hom-Lie algebras, investigates their properties, and provides criteria for their existence, extending the theory of Hom-Lie algebra quotients.

Findings

Conditions for Hom-Lie algebras to have algebras of quotients

Relationship between Hom-Lie algebras and associative algebras of derivations

Introduction of dense extensions in the context of Hom-Lie algebra quotients

Abstract

In this paper, we introduce the notion of algebras of quotients of Hom-Lie algebras and investigate some properties which can be lifted from a Hom-Lie algebra to its algebra of quotients. We also give some necessary and sufficient conditions for Hom-Lie algebras having algebras of quotients. We also examine the relationship between a Hom-Lie algebra and the associative algebra generated by inner derivations of the corresponding Hom-Lie algebra of quotients. Moreover, we introduce the notion of dense extensions and get a proposition about Hom-Lie algebras of quotients via dense extensions.