On $(n+1)$-Hom-Lie Algebras Induced by $n$-Hom-Lie Algebras

TL;DR

This paper investigates the structural relationships between n-Hom-Lie algebras and their induced (n+1)-Hom-Lie algebras, focusing on properties like ideals, solvability, and cohomology.

Contribution

It provides a comprehensive theoretical framework for understanding how n-Hom-Lie algebras induce (n+1)-Hom-Lie algebras and explores their structural properties.

Findings

Established connections between n-Hom-Lie and (n+1)-Hom-Lie algebra structures

Analyzed ideals, centers, and derived series in induced algebras

Explored cohomology and extension properties

Abstract

The purpose of this paper is to study the relationships between an $n$-Hom-Lie algebra and its induced $(n+1)$-Hom-Lie algebra. We provide an overview of the theory and explore the structure properties such as ideals, center, derived series, solvability, nilpotency, central extensions, and the cohomology.