On the deformations and derivations of $n$-ary multiplicative Hom-Nambu-Lie superalgebras

TL;DR

This paper introduces and constructs classes of $n$-ary multiplicative Hom-Nambu-Lie superalgebras, explores their derivations, and develops a deformation theory based on cohomology.

Contribution

It generalizes derivations and deformation theory to $n$-ary multiplicative Hom-Nambu-Lie superalgebras, expanding their mathematical framework.

Findings

Constructed three classes of $n$-ary multiplicative Hom-Nambu-Lie superalgebras.

Extended derivation concepts to superalgebras.

Developed a deformation theory using cohomology.

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.