Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras

TL;DR

This paper introduces a method to construct higher-order Hom-Nambu-Lie algebras from existing ones using trace functions and explores conditions for deriving new Lie algebras from n-Lie algebras with specific forms.

Contribution

It provides a novel construction procedure for (n+1)-Hom-Nambu-Lie algebras and investigates the generation of (n+k)-Lie algebras from n-Lie algebras with k-forms.

Findings

Construction method for (n+1)-Hom-Nambu-Lie algebras from n-Hom-Nambu-Lie algebras.

Conditions relating trace functions and twisting maps for algebra compatibility.

Feasibility of defining (n+k)-Lie algebras from n-Lie algebras with certain k-forms.

Abstract

We present a procedure to construct (n+1)-Hom-Nambu-Lie algebras from n-Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n+k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions.