A non-abelian tensor product of algebras with bracket

TL;DR

This paper introduces a non-abelian tensor product for algebras with bracket, exploring its properties and applications to universal central extensions and homology of perfect algebras.

Contribution

It defines a new non-abelian tensor product for algebras with bracket and analyzes its role in algebraic extensions and homology theories.

Findings

Established properties of the non-abelian tensor product

Connected the tensor product to universal central extensions

Explored implications for low-dimensional homology

Abstract

We introduce and study a non-abelian tensor product of two algebras with bracket with compatible actions on each other. We investigate its applications to the universal central extensions and the low-dimensional homology of perfect algebras with bracket.