Quasi-filiform Leibniz algebras of maximum length

TL;DR

This paper classifies quasi-filiform Leibniz algebras of maximum length with nilindex n-2, completing the understanding of maximum length Leibniz algebras for nilindex up to n-2.

Contribution

It provides a classification of quasi-filiform Leibniz algebras of maximum length in the case where the characteristic sequence is (n-2,2), extending previous results.

Findings

Classification of quasi-filiform Leibniz algebras of maximum length with characteristic sequence (n-2,2)

Completes the study of maximum length Leibniz algebras with nilindex n-p for p ≤ 2

Identifies two characteristic sequences for Leibniz algebras with nilindex n-2

Abstract

The $n$-dimensional $p$-filiform Leibniz algebras of maximum length have already been studied with $0\leq p\leq 2$. For Lie algebras whose nilindex is equal to $n-2$ there is only one characteristic sequence, $(n-2,1,1)$, while in Leibniz theory we obtain two possibilities: $(n-2,1,1)$ and $(n-2,2)$. The first case (the 2-filiform case) is already known. The present paper deals with the second case, i.e., quasi-filiform non Lie Leibniz algebras of maximum length. Therefore this work completes the study of maximum length of Leibniz algebras with nilindex $n-p$ with $0 \leq p \leq 2$.