Representations and cohomolgies of Rota-Baxter 3-Lie algebras

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.