| In this master thesis,we first determine the even Rota-Baxter operators of weight 1 on the Lie superalgebras q(2)over the field of complex numbers C.Using the even part of q(2)to be isomorphic to gl(2,C)=sl(2,C)⊕C,by two RotaBaxter operators P5 and P12 that are known to be obliquely symmetric with a weight of 1 in Lie algebras sl(2,C),the problem of solving the even Rota-Baxter operators with q(2)weight 1 are transformed into the problem of solving the solution of multivariate quadratic equations,and then we are able to obtain 3 kinds of the even Rota-Baxter operators on q(2)based on P5 of weight 1,30 kinds of the even Rota-Baxter operators on q(2)based on P12 of weight 1. |
