On the deformations and derivations of $n$-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.

14. arXiv admin note: text overlap with arXiv:1401.0378

References in corpus (5)

• Deformations of Lie Algebras using $\sigma$-derivations
• Representations of hom-Lie algebras
• Hom-algebras and homology
• Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras
• On the cohomology and extensions of $n$-ary multiplicative Hom-Nambu-Lie superalgebras