Rota-baxter Operators Of Low Dimensional Queer Lie Superalgebras

In the Lie superalgebras cases,the Rota-Baxter operators of weight 0 are the so-lutions of the classical Yang-Baxter equations,the Rota-Baxter operators of weight 1 are the solutions of the deformed Yang-Baxter equations.Therefore,it is signifi-cant to study the Rota-Baxter operators on the Lie superalgebras.In this paper,we first determine all the Rota-Baxter operators on the Lie superalgebra q(1)over the field of complex numbers C.Secondly,we determine the even Rota-Baxter operators of weight 0 on the Lie superalgebra q(2)over the field of complex numbers C.For the q(2)case,through there exit three kinds P10,P15 and P20 of Rota-Baxter operators of weight 0 on the Lie algebra sl[(2,C),using the even part of q(2)to be isomorphic to gl(2,C)=sl(2,C)?C,then,the Rota-Baxter operator for solving Lie superalgebra turns out to the problem of solving quadratic equations of several variables,we are able to obtain 31 kinds of the even Rota-Baxter operators on q(2)based on P10 of weight 0,18 kinds of the even Rota-Baxter operators on q(2)based on P15 of weight 0 and 10 kinds of the even Rota-Baxter operators on q(2)based on P20 of weight 0.