A Class Of Baxter Algebra And Its Applications

This paper we commence to study the Rota-Baxter operator of weight zeroon3-dimension and4-dimension complex pre-Lie algebras. Such operators satisfy(the operator from of) the classical Yang-Baxter equation on the sub-adjacent Liealgebras of the pre-Lie algebras. We not only study the invertible Rota-Baxteroperator on pre-Lie algebras, but also give some interesting construction of Rota-Baxter operator. We also study the relationshiip of Rota-Baxter operator whenweight is diferent.This paper first give some definition and basic properties related to Baxteralgebra in chapter2. Then in the third chapter, give the equation which Rota-Baxter operator should satisfy when it represented by matrix, and the relationshipbetween the operators when weight is changed. In the chapter4of this paper, westudy the Rota-Baxter operators on upper triangular a matrice algebras of order2. In the chapter5of this paper, we study the Rota-Baxter operators on matricealgebras of order2. This generalizes the result of the correlative literature.