摘要：In this paper, we discuss the representations of n -ary multiplicative Hom-Nambu-Lie superalgebras as a generalization of the notion of representations for n -ary multiplicative Hom-Nambu-Lie algebras. We also give the cohomology of an n -ary multiplicative Hom-Nambu-Lie superalgebra and obtain a relation between extensions of an n -ary multiplicative Hom-Nambu-Lie superalgebra b by an abelian one a and Z 1 b , a 0 ¯ . We also introduce the notion of T ∗ -extensions of n -ary multiplicative Hom-Nambu-Lie superalgebras and prove that every finite-dimensional nilpotent metric n -ary multiplicative Hom-Nambu-Lie superalgebra over an algebraically closed field of characteristic not 2 in the case α is a surjection is isometric to a suitable T ∗ -extension.
