Rota-Baxter Operators On The Lie Superalgebra Sl(2,1)

We study the even Rota-Baxter operators of weight zero on the Lie superalgebra sl(2,1).We have seen from[18]that there exits two families P10 and P15 of Rota-Baxter operators on the semisimple Lie algebra sl(2,C).The purpose of this thesis is to calculate the even Rota-Baxter operators of weight zero onsL(2,1)based on P10 and P15.More pre-cisely,we can derive 10 families of the Rota-Baxter operators for P10 and 19 families for P15.