Rota-baxter3-lie Algebras

In recent years, Rota-Baxter operator is widely applied in many fields of mathemat-ics and physics, such as combinatorial mathematics, number theory and quantum fieldtheory, etc.In the paper we define Rota-Baxter operators and diferential operators of weightλ on n-algebras, and then provide the definition of Rota-Baxter3-Lie algebras. ByRota-Baxter Lie algebras, Rota-Baxter pre-Lie algebras and Rota-Baxter commutativeassociative algebras etc, we construct Rota-Baxter3-Lie algebras. We also introducethe concept of Rota-Baxter Lie triple system, and on the basis of Rota-Baxter3-Liealgebras, from the Rota-Baxter Lie triple system, we realize the new Rota-Baxter Lietriple system. The paper is organized as follows,In section1, we introduce the basic concepts and notations that are needed in thepaper.Section2gives the concepts of diferential n-algebra and Rota-Baxter n-algebra andstudy their algebraic properties.In section3, we realize the Rota-Baxter3-Lie algebras by Rota-Baxter Lie algebra,Rota-Baxter pre-Lie algebra, Rota-Baxter commutative associative algebras and linearfunction, derivation, Rota-Baxter operator.Section4studies its structure and property, by Rota-Baxter3-Lie algebra we canget new Rota-Baxter3-Lie algebra.Section5gives the concept of Rota-Baxter Lie triple system, and study its realiza-tion.