On classification of Filiform Hom-Lie algebras

TL;DR

This paper introduces and classifies nilpotent and filiform Hom-Lie algebras, extending existing methods to Hom-type algebras and providing a detailed classification for dimensions up to seven.

Contribution

It extends the classification framework of filiform Lie algebras to Hom-Lie algebras, covering dimensions up to seven.

Findings

Classification of filiform Hom-Lie algebras for dimensions n ≤ 7

Extension of Vergne and Khakimdjanov's approach to Hom-type algebras

New structural insights into nilpotent Hom-Lie algebras

Abstract

The purpose of this paper is to introduce and study nilpotent and filiform Hom-Lie algebras. Moreover, we extend Vergne and Khakimdjanov's approach to Hom-type algebras and provide a classification of filiform Hom-Lie algebras of dimension $n,n\leq7$.