# Solvable Leibniz algebras with naturally graded non-Lie $p$-filiform nilradicals and maximal complemented space of its nilradical

## TL;DR

This paper classifies solvable Leibniz algebras with specific naturally graded non-Lie nilradicals and maximal complemented spaces, identifying rigid and complete cases to advance understanding of their structure.

## Contribution

It provides a classification of such Leibniz algebras up to isomorphism, including the identification of rigid and complete algebras, which was previously unexplored.

## Key findings

- Classification of solvable Leibniz algebras with given nilradicals
- Identification of rigid and complete algebras within this class
- Description of these algebras up to isomorphism

## 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 $p$-filiform non-Lie Leibniz algebra $(n-p\geq4)$ and the complemented space to nilradical has maximal dimension, are described up to isomorphism. Moreover, among obtained algebras we indicate the rigid and complete algebras