Representations and cohomology of n -ary multiplicative Hom–Nambu–Lie algebras

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 derivation 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.