Minimal nonnilpotent Leibniz algebras

TL;DR

This paper classifies a special class of solvable Leibniz algebras where all proper subalgebras are nilpotent, extending previous Lie algebra results and highlighting differences between Leibniz and Lie algebra structures.

Contribution

It provides a complete classification of minimal nonnilpotent solvable Leibniz algebras, generalizing existing Lie algebra classifications and illustrating key structural differences.

Findings

Classification of all nonnilpotent, solvable Leibniz algebras with nilpotent proper subalgebras

Examples demonstrating differences between Leibniz and Lie algebra cases

Extension of previous Lie algebra results to Leibniz algebras

Abstract

We classify all nonnilpotent, solvable Leibniz algebras with the property that all proper subalgebras are nilpotent. This generalizes the work of Stitzinger and Towers in Lie algebras. We show several examples which illustrate the differences between the Lie and Leibniz results.