Tensor square and isoclinic extensions of multiplicative Lie algebras

TL;DR

This paper explores the properties of tensor squares and isoclinic extensions in multiplicative Lie algebras, establishing new theoretical results and relationships among covers and isoclinic structures.

Contribution

It introduces the concept of isoclinic extensions for multiplicative Lie algebras and proves that covers of such algebras are mutually isoclinic.

Findings

Covers of multiplicative Lie algebras are mutually isoclinic

Developed the concept of isoclinic extensions

Established several new theoretical results

Abstract

In this paper, we discuss the capable and isoclinic properties of the tensor square in the context of multiplicative Lie algebras. We also developed the concept of isoclinic extensions and proved several results for multiplicative Lie algebras. Consequently, we demonstrate that covers of a multiplicative Lie algebra are mutually isoclinic.