Maximal solvable Leibniz algebras whose nilradical is a quasi-filiform algebra

TL;DR

This paper classifies maximal solvable Leibniz algebras with a specific type of nilradical, a naturally graded quasi-filiform algebra, focusing on those with the largest possible complement space.

Contribution

It provides a classification of such Leibniz algebras up to isomorphism, expanding understanding of their structure with a maximal complement dimension.

Findings

Classification of maximal solvable Leibniz algebras with a quasi-filiform nilradical

Description of these algebras up to isomorphism

Identification of the maximal dimension of the complemented space

Abstract

The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded quasi-filiform algebra and the complemented space to the nilradical has maximal dimension, are described up to isomorphism.