Abstract
We show that given a hom-Lie algebra one can construct the n-ary hom-Lie bracket by means of an 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.