Solvable extensions of the naturally graded quasi-filiform Leibniz algebras

TL;DR

This paper classifies certain solvable Leibniz algebras with a specific nilradical structure, focusing on those with a one-dimensional complement to the nilradical, expanding understanding of their algebraic properties.

Contribution

It provides a classification of solvable Leibniz algebras with naturally graded quasi-filiform nilradicals and one-dimensional complements, a specific case not fully explored before.

Findings

Complete classification up to isomorphism

Identification of algebraic structures with given nilradical

Extension of known algebraic frameworks

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 one dimension, are described up to isomorphism.