Almost inner derivations of some nilpotent Leibniz algebras

TL;DR

This paper studies almost inner derivations in finite-dimensional nilpotent Leibniz algebras, revealing cases where these derivations differ from inner derivations, especially in filiform non-Lie and Lie-containing algebras.

Contribution

It demonstrates the existence of almost inner derivations distinct from inner derivations in certain nilpotent Leibniz algebras, expanding understanding of their structure.

Findings

Almost inner derivations differ from inner derivations in some filiform non-Lie Leibniz algebras.

In some filiform Leibniz algebras containing Lie algebras, almost inner derivations do not coincide with inner derivations.

The study highlights structural differences in derivations within specific classes of Leibniz algebras.

Abstract

We investigate almost inner derivations of some finite-dimensional nilpotent Leibniz algebras. We show the existence of almost inner derivations of Leibniz filiform non-Lie algebras differing from inner derivations, we also show that the almost inner derivations of some filiform Leibniz algebras containing filiform Lie algebras do not coincide with inner derivations.