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Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras. (English) Zbl 1368.17004
Summary: In this paper, we introduce the concepts of Rota-Baxter operators and differential operators with weights on a multiplicative \(n\)-ary Hom-algebra. We then focus on Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras and show that they can be derived from Rota-Baxter Hom-Lie algebras, Hom-preLie algebras and Rota-Baxter commutative Hom-associative algebras. We also explore the connections between these Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras.

MSC:
17A42 Other \(n\)-ary compositions \((n \ge 3)\)
17B99 Lie algebras and Lie superalgebras
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