Post-Lie Superalgebra Structure And Rota-Baxter Operator On Lie Superalgebra S(2)

The Post-Lie superalgebra structures and Rot a-Baxter operators on the Lie superalgebra S(2)are investigated in this paper.Firstly,we obtain the matrix sets of Post-Lie superalgebras on the Lie superalgebra S(2)which there are 31 classes.Secondly,we use the isomorphism between S(2)(?) and sl(2,C)to obtain that there are 36 classes of the even Rota-Baxter operators with weight zero on the Lie superalgebra S(2).Finally,we prove that there are 20 classes of the odd Rota-Baxter operators with weight zero on the Lie superalgebra S(2).