Solvable Leibniz algebras with quasi-filiform Lie algebras of maximum length nilradicals

TL;DR

This paper classifies solvable Leibniz algebras with a specific type of nilradical, proving their rigidity when complemented by a two-dimensional space, advancing understanding of their structure.

Contribution

It provides a classification of these Leibniz algebras and establishes their rigidity in certain cases, which is a new insight in the field.

Findings

Classification of solvable Leibniz algebras with quasi-filiform Lie nilradicals

Proof of rigidity for algebras with two-dimensional complements

Enhanced understanding of algebraic structure and stability

Abstract

In this paper solvable Leibniz algebras whose nilradical is quasi-filiform Lie algebra of maximum length, are classified. The rigidity of such Leibniz algebras with two-dimensional complemented space to nilradical is proved.