The classification of non-characteristically nilpotent filiform Leibniz algebras

TL;DR

This paper classifies non-characteristically nilpotent filiform Leibniz algebras by analyzing derivations, providing conditions for nilpotency, and utilizing Catalan numbers for the first family.

Contribution

It introduces a classification of non-characteristically nilpotent filiform Leibniz algebras across three families, with new criteria and combinatorial methods.

Findings

Identified sufficient conditions for characteristically nilpotent algebras.

Classified non-characteristically nilpotent algebras in the first family using Catalan numbers.

Described non-characteristically nilpotent algebras in the remaining two families.

Abstract

In this paper we investigate the derivations of filiform Leibniz algebras. Recall that the set of filiform Leibniz algebras of fixed dimension is decomposed into three non-intersected families. We found sufficient conditions under which filiform Leibniz algebras of the first family are characteristically nilpotent. Moreover, for the first family we classify non-characteristically nilpotent algebras by means of Catalan numbers. In addition, for the rest two families of filiform Leibniz algebras we describe non-characteristically nilpotent algebras, i.e., those filiform Leibniz algebras which lie in the complementary set to those characteristically nilpotent.