Solvable extensions of the naturally graded quasi-filiform Leibniz algebra of second type $\mathcal{L}^2$

TL;DR

This paper classifies all possible solvable extensions of a specific naturally graded quasi-filiform Leibniz algebra, providing a comprehensive understanding of its structure and role as a nilradical in solvable Leibniz algebras.

Contribution

It constructs all right and left solvable indecomposable extensions of the algebra, identifying its role as a nilradical in solvable Leibniz algebras.

Findings

Complete classification of solvable extensions over br

Identification of the algebra as a nilradical in solvable Leibniz algebras

Explicit construction of indecomposable extensions

Abstract

For a sequence of the naturally graded quasi-filiform Leibniz algebra of second type $\mathcal{L}^2$ introduced by Camacho, G\'{o}mez, Gonz\'{a}lez and Omirov, all possible right and left solvable indecomposable extensions over the field $\Bbb R$ are constructed so that the algebra serves as the nilradical of the corresponding solvable Leibniz algebras we find in the paper.