Classification of solvable Leibniz algebras with null-filiform nilradical

TL;DR

This paper classifies a specific type of solvable Leibniz algebras with null-filiform nilradicals and extends the classification to decompositions involving direct sums, providing a detailed structural understanding.

Contribution

It provides a new classification of solvable Leibniz algebras with null-filiform nilradicals and analyzes their decompositions and ideal structures.

Findings

Classification of solvable Leibniz algebras with null-filiform nilradicals

Extension to direct sum decompositions with one-dimensional complements

Identification of ideals within these algebra structures

Abstract

In this paper we classify solvable Leibniz algebras whose nilradical is a null-filiform algebra. We extend the obtained classification to the case when the solvable Leibniz algebra is decomposed as a direct sum of its nilradical, which is a direct sum of null-filiform ideals, and a one-dimensional complementary subspace. Moreover, in this case we establish that these ideals are ideals of the algebra, as well.