Solvable Leibniz algebras with naturally graded non-Lie $p$-filiform nilradicals

TL;DR

This paper classifies certain solvable Leibniz algebras with specific nilradicals and studies their properties, including rigidity, expanding understanding of their structure and deformations.

Contribution

It provides a detailed description of solvable Leibniz algebras with naturally graded non-Lie $p$-filiform nilradicals and analyzes their rigidity and structural properties.

Findings

Classification of solvable Leibniz algebras with given nilradicals

Proof of rigidity for algebras with maximal complemented space

Analysis of algebras with abelian nilradicals and extremal dimensions

Abstract

In this paper solvable Leibniz algebras with naturally graded non-Lie $p$-filiform $(n-p\geq4)$ nilradical and with one-dimensional complemented space of nilradical are described. Moreover, solvable Leibniz algebras with abelian nilradical and extremal (minimal, maximal) dimensions of complemented space nilradical are studied. The rigidity of solvable Leibniz algebras with abelian nilradical and maximal dimension of its complemented space is proved.