Generalized Derivations and Rota-Baxter Operators of $$\varvec{n}$$-ary Hom-Nambu Superalgebras

Abstract

The aim of this paper is to generalise the construction of n-ary Hom-Lie bracket by means of an $$(n-2)$$ ( 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.

On Hom-Nambu-Poisson superalgebras structures and their representations

“…In [24], the authors introduced a construction of n-Hom-Lie superalgebra by a Hom-Lie superalgebra in which they gave an n-ary product defined by (2.8) [x 1 , . .…”

“…Theorem 2.1. [24] Let (A, [•, •], α) be a multiplicative Hom-Lie superalgebra, A * its dual and φ be an even cochain of degree n − 2, i.e. φ ∈ ∧ n−2 A * .…”