Isoclinic Lie Crossed Modules

TL;DR

This paper introduces the concept of isoclinism for Lie crossed modules, explores their fundamental properties, and examines the relationship between class preserving actors and isoclinism in this context.

Contribution

It presents the first study of isoclinism in Lie crossed modules and defines class preserving actors, establishing new theoretical connections.

Findings

Defined isoclinism for Lie crossed modules

Analyzed properties of Lie crossed modules under isoclinism

Explored the relation between class preserving actors and isoclinism

Abstract

We introduce the notion of isoclinism among crossed modules of Lie algebras, which will be called "Lie crossed modules" hereafter, and investigate some basic properties. Additionally, we introduce the notion of class preserving actor of a Lie crossed module and the relation with isoclinism.