# Leibniz A-algebras

## TL;DR

This paper extends the concept of A-algebras from Lie algebras to Leibniz algebras, exploring their properties and significance in mathematical physics and algebraic structures.

## Contribution

It generalizes known results about A-algebras to Leibniz algebras, broadening the understanding of their structure and applications.

## Key findings

- Generalized A-algebra properties to Leibniz algebras
- Connected Leibniz A-algebras to Lie algebra results
- Enhanced understanding of Leibniz algebra structures

## Abstract

A finite-dimensional Lie algebra is called an A-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras.