Rota-Baxter Superalgebras

The main purpose of this paper is to define Rota-Baxter superalgebras. The author applies Rota-Baxter superalgebras to construct pre Lie superalgebras, dendriform superalgebras, Leibniz Poisson superalgebras and other algebras. In particular, the properties of Rota-Baxter superoperators are studied. The author also uses Rota-Baxter superoperators to construct dendriform superalgebras.Furthermore, this paper presents the examples of Leibniz superalgebras and Leibniz Poisson superalgebras, the methods of constructing Leibniz superalgebras and Leibniz Poisson superalgebras, and shows how to use dendriform superalgebras to construct pre Lie superalgebras and Leibniz Poisson superalgebras.