Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras

TL;DR

This paper develops a cohomology theory for n-ary Hom-Nambu-Lie algebras, extending concepts of derivations and representations, and links their cohomology to that of Hom-Leibniz algebras, aiding understanding of their extensions and deformations.

Contribution

It generalizes derivations and representations to n-ary Hom-Nambu-Lie algebras and connects their cohomology to Hom-Leibniz algebra cohomology, advancing the theoretical framework.

Findings

Cohomology of n-ary Hom-Nambu-Lie algebras derived from Hom-Leibniz cohomology

Framework for central extensions and deformations of these algebras

Extension of derivations and representations concepts to n-ary structures

Abstract

The aim of this paper is to provide cohomologies of $n$-ary Hom-Nambu-Lie algebras governing central extensions and one parameter formal deformations. We generalize to $n$-ary algebras the notions of derivations and representation introduced by Sheng for Hom-Lie algebras. Also we show that a cohomology of $n$-ary Hom-Nambu-Lie algebras could be derived from the cohomology of Hom-Leibniz algebras.