Rota - Baxter Operators On A Class Of Lie Algebras

From the last century scientists found the Baxter Algebra to now, Rota-Baxter operator in many natural disciplines are widely used. At the same time, Lie algebra is kind of characteristics to features of algebra. Therefore, This thesis studies the structure of operator Abel Lie algebra and summarizes the properties of the RotaBaxter operator defines the new pre-Lie algebra.Firstly, this thesis introduces the preliminary knowledge related to the Lie algebra and Rota-Baxter operator. Then study the structure of the Rota-Baxter operator of weight 0, discussion and summarize the Rota-Baxter operator of weight 0 on K[x] and give specific examples, In the end, introduce the properties of the RotaBaxter operator of weight 1 on Abel Lie algebra, and with Rota-Baxter operator of weight 1 constructed a new pre-Lie algebras.