Isoclinic relative central extensions of a pair of regular Hom-Lie algebras

TL;DR

This paper explores the structure of isoclinic relative central extensions in Hom-Lie algebras, establishing relations and classifications within their isoclinism families.

Contribution

It introduces the concept of isoclinism for relative central extensions of Hom-Lie algebras and characterizes isomorphisms within these classes.

Findings

Defined isoclinism for relative central extensions of Hom-Lie algebras

Established relations among extensions in an isoclinism family

Characterized isomorphisms within isoclinism classes

Abstract

In this paper, we show the relation among the relative central extensions in an isoclinism family of a particular relative central extension of Hom-Lie algebras. We define the notion of isoclinism on the central relative extensions of a pair of Hom-Lie algebras. Then, we figure out the concept of isomorphism in the equivalence class of isoclinisms on the central relative extensions of a pair of Hom-Lie algebras.