Solvable Leibniz algebras with filiform nilradical

TL;DR

This paper extends the classification of solvable Leibniz algebras with filiform nilradicals, showing that those with filiform Lie nilradicals are actually Lie algebras, thus deepening understanding of their structure.

Contribution

It generalizes previous classifications by describing solvable Leibniz algebras with arbitrary filiform nilradicals and proves that those with filiform Lie nilradicals are Lie algebras.

Findings

Solvable Leibniz algebras with filiform Lie nilradicals are Lie algebras.

Extended classification of solvable Leibniz algebras with filiform nilradicals.

Established structural properties of these algebras.

Abstract

In this paper we continue the description of solvable Leibniz algebras whose nilradical is a filiform algebra. In fact, solvable Leibniz algebras whose nilradical is a naturally graded filiform Leibniz algebra are described in \cite{Campo} and \cite{SolGFil}. Here we extend the description to solvable Leibniz algebras whose nilradical is a filiform algebra. We establish that solvable Leibniz algebras with filiform Lie nilradical are Lie algebras.