Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras

TL;DR

This paper studies pre-derivations of filiform Leibniz algebras, classifies their structures in specific families, and identifies conditions for strong nilpotency and characteristically nilpotent cases.

Contribution

It provides the first detailed description of pre-derivations for two families of filiform Leibniz algebras and characterizes their nilpotency properties.

Findings

Described pre-derivations for the first and second families.

Established conditions for strong nilpotency.

Characterized non-strongly nilpotent, characteristically nilpotent algebras.

Abstract

In this paper we investigate pre-derivations of filiform Leibniz algebras. Recall that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three non-intersected families. We describe the pre-derivation of filiform Leibniz algebras for the first and second families. We found sufficient conditions under which filiform Leibniz algebras are strongly nilpotent. Moreover, for the first and second families, we give the description of characteristically nilpotent algebras which are non-strongly nilpotent.