Classifying Several Classes of Leibniz Algebras

TL;DR

This paper extends classification results from Lie algebras to Leibniz algebras, identifying unique types and providing a comprehensive classification of certain Leibniz algebra classes.

Contribution

It introduces new classifications for minimal non-elementary Leibniz algebras and those with a unique maximal ideal, including types without Lie algebra analogues.

Findings

Classified minimal non-elementary Leibniz algebras

Classified Leibniz algebras with a unique maximal ideal

Provided a classification of E-Leibniz algebras

Abstract

We extend results related to maximal subalgebras and ideals from Lie to Leibniz algebras. In particular, we classify minimal non-elementary Leibniz algebras and Leibniz algebras with a unique maximal ideal. In both cases, there are types of these algebras with no Lie algebra analogue. We also give a classification of E-Leibniz algebras which is very similiar to its Lie algebra counterpart.