On the Deformations and Derivations ofn-Ary Multiplicative Hom-Nambu-Lie Superalgebras

Abstract

In this paper, we introduce the relevant concepts of n-ary multiplicative Hom-Nambu-Lie superalgebras and construct three classes of n-ary multiplicative Hom-Nambu-Lie superalgebras. As a generalization of the notion of derivations for n-ary multiplicative Hom-Nambu-Lie algebras, we discuss the derivations of n-ary multiplicative Hom-Nambu-Lie superalgebras. In addition, the theory of one parameter formal deformation of n-ary multiplicative Hom-Nambu-Lie superalgebras is developed by choosing a suitable cohomology.

$n$-ary Hom-Nambu algebras

“…In this paper, the main result is to study ω-derivations of a vector space, and how to structure a new n-ary Hom-Nambu algebra. In addition, we also introduce the derivations and representations similar with n-ary multiplicative Hom-Nambu-Lie superalgebras and n-Lie superalgebras in [4,6] as its application.…”