Classification of solvable Leibniz algebras with abelian nilradical and $k-1$ dimensional extension

TL;DR

This paper classifies all solvable Leibniz algebras with an abelian nilradical and a specific dimensional extension, providing a comprehensive understanding of their structure in the case where the nilradical is abelian.

Contribution

It offers a complete classification of solvable Leibniz algebras with abelian nilradicals and a $(k-1)$-dimensional extension, extending previous work in the field.

Findings

Classification of all such Leibniz algebras achieved

Explicit descriptions of algebra structures provided

Framework for understanding extensions of abelian nilradicals

Abstract

This work is devoted to the classification of solvable Leibniz algebras with an abelian nilradical. We consider $k-1$ dimensional extension of $k$-dimensional abelian algebras and classify all $2k-1$-dimensional solvable Leibniz algebras with an abelian nilradical of dimension $k$.