On nilpotency in Leibniz algebras

TL;DR

This paper proves that right nilpotent Leibniz algebras are also strongly nilpotent, with an explicit bound on the degree of strong nilpotency related to the degree of right nilpotency.

Contribution

It establishes a quantitative relationship between right nilpotency and strong nilpotency in Leibniz algebras, providing a new bound on the latter.

Findings

Right nilpotent Leibniz algebras are strongly nilpotent.

The degree of strong nilpotency is at most 4n^2 - 2n + 1 for a right nilpotent algebra of degree n.

The result offers a concrete bound linking two types of nilpotency in Leibniz algebras.

Abstract

The main result of this paper is to prove that if a (right) Leibniz algebra $L$ is \textit{right nilpotent} of degree $n$, then $L$ is \textit{strongly nilpotent} of degree less or equal to $4n^2-2n+1$.