Some Constructions of Multiplicative n -ary hom–Nambu Algebras

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 the given hom–Lie algebra and find the conditions under which this n-ary bracket satisfies the Filippov–Jacobi identity, thereby inducing the structure of n-hom–Lie algebra. We introduce the notion of a hom–Lie n-tuple system which is the generalization of a hom–Lie triple system. We construct hom–Lie n-tuple system using a hom–Lie algebra.