Universal imbedding of a Hom-Lie Triple System

TL;DR

This paper constructs a universal embedding for regular Hom-Lie triple systems into Lie algebras, establishing an equivalence of categories and characterizing the subcategory involved.

Contribution

It introduces a universal embedding of regular Hom-Lie triple systems into Lie algebras and characterizes the related categorical structures.

Findings

Established a universal embedding into Lie algebras

Proved categorical equivalence with a subcategory of graded Lie algebras

Provided characterizations of the subcategory

Abstract

In this article we will build a universal imbedding of a regular Hom- Lie triple system into a Lie algebra and show that the category of regular Hom-Lie triple systems is equivalent to a full subcategory of pairs of $\mathbb{Z}/2\mathbb{Z}$- graded Lie algebras and Lie algebra automorphism, then finally give some characterizations of this subcategory.