Multiplicative Lie Algebra Structures on a Group

TL;DR

This paper classifies all possible multiplicative Lie algebra structures on a given group and explores how homomorphisms from the non-abelian exterior square relate to these structures.

Contribution

It provides a classification of multiplicative Lie algebra structures on groups and links these structures to homomorphisms from the non-abelian exterior square.

Findings

Classification of multiplicative Lie algebra structures up to isomorphism.

Every homomorphism from the non-abelian exterior square to the group induces a multiplicative Lie algebra structure under certain conditions.

Establishes conditions under which these structures are equivalent.

Abstract

The main aim of this paper is to classify the distinct multiplicative Lie algebra structures (up to isomorphism) on a given group. We also see that for a given group $G$, every homomorphism from the non-abelian exterior square $G \wedge G$ to $G$ gives a multiplicative Lie algebra structure on $G$ under certain conditions.