Abelian extensions of five-dimensional solvable Leibniz algebras

TL;DR

This paper classifies one-dimensional abelian extensions of five-dimensional solvable Leibniz algebras with specific nilradicals, expanding understanding of their structure and extension properties.

Contribution

It introduces a complete classification method for certain abelian extensions of five-dimensional solvable Leibniz algebras, including cases with null-filiform nilradicals.

Findings

Complete classification of extensions with three-dimensional nilradical.

Uniqueness of abelian extension when nilradical is null-filiform.

Extension method adapted for solvable Leibniz algebras.

Abstract

In this work, we extend the central extension method for solvable Leibniz algebras. Using this method, a complete classification of one-dimensional abelian extensions of five-dimensional solvable Leibniz algebras with a non-trivial three-dimensional nilradical is obtained. Furthermore, we explore extensions of solvable Leibniz algebras whose nilradical is null-filiform, establishing that, in this case, there exists a unique solvable abelian extension.