Some constructions of multiplicative $n$-ary Hom-Nambu algebras

TL;DR

This paper presents methods to construct multiplicative n-ary Hom-Nambu algebras from Hom-Lie algebras, establishing conditions for their algebraic identities and introducing a generalized Hom-Lie n-uplet system.

Contribution

It introduces new constructions of n-Hom-Lie algebras from Hom-Lie algebras and defines the Hom-Lie n-uplet system as a generalization of Hom-Lie triple systems.

Findings

Constructed n-ary Hom-Lie brackets from Hom-Lie algebras.

Identified conditions for the Filippov-Jacobi identity in these constructions.

Introduced the Hom-Lie n-uplet system as a generalization.

Abstract

We show that given a Hom-Lie algebra one can construct the n-ary Hom-Lie bracket by means of an (n-2)-cochain of given Hom-Lie algebra and find the conditions under which this n-ary bracket satisfies the Filippov-Jacobi identity, there by inducing the structure of n-Hom-Lie algebra. We introduce the notion of Hom-Lie $n$-uplet system which is the generalization of Hom-Lie triple system. We construct Hom-Lie $n$-uplet system using a Hom-Lie algebra.