# Solvable extensions of the naturally graded quasi-filiform Leibniz algebra of second type $\mathcal{L}^4$

## TL;DR

This paper classifies all right solvable indecomposable extensions of a specific naturally graded quasi-filiform Leibniz algebra of second type, expanding understanding of its algebraic structure.

## Contribution

It provides a complete classification of solvable extensions of the algebra $ ext{L}^4$, a previously studied algebraic structure, revealing new algebraic configurations.

## Key findings

- All possible right solvable indecomposable extensions are constructed.
- The classification enhances understanding of the algebra's extension properties.
- Results contribute to the theory of Leibniz algebra extensions.

## Abstract

For a sequence of the naturally graded quasi-filiform Leibniz algebra of second type $\mathcal{L}^4$ introduced by Camacho, G\'{o}mez, Gonz\'{a}lez and Omirov, all the possible right solvable indecomposable extensions over the field $\Bbb C$ are constructed.