Generalized Derivations and Rota-Baxter Operators of $$\varvec{n}$$-ary Hom-Nambu Superalgebras
Sami Mabrouk, Othmen Ncib, Sergei Silvestrov
Abstract
Abstract The aim of this paper is to generalise the construction of n -ary Hom-Lie bracket by means of an $$(n-2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -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.