Generalized Derivations and Rota-Baxter Operators of n-ary Hom-Nambu Superalgebras

The aim of this paper is to generalise the construction of n -ary Hom-Lie bracket by means of an ( n - 2 ) -cochain of given Hom-Lie algebra to super case inducing n -Hom-Lie superalgebras. We study the notion of generalized derivations and Rota-Baxter operators of n -ary Hom-Nambu and n -Hom-Lie superalgebras and their relation with generalized derivations and Rota-Baxter operators of Hom-Lie superalgebras. We also introduce the notion of 3-Hom-pre-Lie superalgebras which is the generalization of 3-Hom-pre-Lie algebras.