Rota-Baxter 3-Lie algebras

TL;DR

This paper introduces Rota-Baxter operators on n-algebras, focusing on Rota-Baxter 3-Lie algebras, and explores their derivation from other algebraic structures and inheritance properties.

Contribution

It defines Rota-Baxter operators on n-algebras and constructs Rota-Baxter 3-Lie algebras from related algebraic frameworks, revealing their inheritance properties.

Findings

Rota-Baxter 3-Lie algebras can be derived from Rota-Baxter Lie and pre-Lie algebras.

They can also be obtained from Rota-Baxter commutative associative algebras with derivations.

Inheritance properties of Rota-Baxter 3-Lie algebras are established.

Abstract

In this paper we introduce the concepts of a Rota-Baxter operator and a differential operator with weights on an $n$-algebra. We then focus on Rota-Baxter 3-Lie algebras and show that they can be derived from Rota-Baxter Lie algebras and pre-Lie algebras and from Rota-Baxter commutative associative algebras with derivations. We also establish the inheritance property of Rota-Baxter 3-Lie algebras.