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.

中文翻译：

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$$ \ varvec {n} $$ n -ary Hom-Nambu超代数的广义导数和Rota-Baxter算子

本文的目的是通过给定Hom-Lie代数的\（（n-2）\）- cochain泛化n元Hom-Lie括号的构造，从而推广到n -Hom-Lie超代数的超级案例。我们研究广义导和罗塔-巴克斯特运营商的概念ñ进制坎南部和ñ -Hom，李超及其与广义导和坎李超的罗塔-巴克斯特运营商的关系。我们还介绍了3-Hom-pre-Lie超级代数的概念，它是3-Hom-pre-Lie代数的推广。