3-Lie Superalgebras

This article gives the definition of the Rota-Baxter 3-Lie superalgebra and constructs examples of Rota-Baxter 3-Lie superalgebras by Rota-Baxter Lie superalgebras and Rota-Baxter Pre-Lie superalgebras,and gives the methods to construct the Rota-Baxter 3-Lie superalgebra based on two superalgebras and gives the methods to construct Rota-Baxter Lie supertriple systems based on superalgebras.Then,the paper also studys the structure of Rota-Baxter 3-Pre-Lie superalgebras,and gives the ways to construct superalgebras.Finally,this paper gives the definition of Nijenhuis superoperators and proves the connection between Nijenhuis superoperators and trivial deformations.