Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras

TL;DR

This paper introduces Rota-Baxter operators on multiplicative n-ary Hom-algebras, focusing on 3-ary Hom-Nambu-Lie algebras, and explores their derivation from related algebraic structures and their interconnections.

Contribution

It defines Rota-Baxter operators on multiplicative n-ary Hom-algebras and constructs 3-ary Hom-Nambu-Lie algebras from various related algebraic frameworks.

Findings

Rota-Baxter operators are introduced on multiplicative n-ary Hom-algebras.

3-ary Hom-Nambu-Lie algebras are derived from Rota-Baxter Hom-Lie, Hom-preLie, and Rota-Baxter commutative Hom-associative algebras.

Connections between different Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras are established.

Abstract

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.