Representations and cohomolgies of Rota-Baxter 3-Lie algebras

TL;DR

This paper explores the structure, representations, and cohomology theories of Rota-Baxter 3-Lie algebras, including their deformations and extensions, advancing the mathematical understanding of these algebraic systems.

Contribution

It introduces new concepts like representations, matched pairs, and Manin triples for Rota-Baxter 3-Lie algebras, and develops their cohomology and deformation theories.

Findings

Defined representations, matched pairs, and Manin triples for Rota-Baxter 3-Lie algebras

Established cohomology theory for these algebras

Analyzed deformations and central extensions

Abstract

The goal of the present paper is to investigate representations and cohomologies of Rota-Baxter 3-Lie algebras with any weight. We introduce representations, matched pairs and Manin triples of Rota-Baxter 3-Lie algebras. Furthermore, we discuss cohomology theory of Rota-Baxter 3-Lie algebras. The deformations and central extensions of Rota-Baxter 3-Lie algebras are also studied.