The Representation Of A Kind Of Rota-Baxter Algebra

Rota-Baxter algebra appeared in the 1960s.It originated from Baxter's alge-braic study of the integral equation of wave theory in probability theory.Rota-Baxter algebra has important applications in algebra and aroused the interest of many mathematicians.The module of Rota-Baxter algebra is a generalization of the module of associative algebra,which has attracted the attention of scholars in recent years just.In particular,the module structures of a classes of polynomial Rota-Baxter algebras with weight 0 have been studied.In this paper,we will study a classes of polynomial Rota-Baxter algebras with non-zero weights.To be precise,this paper will give some properties of(xk[x],P)-module.In addition,we determine the relation between(xk[x],P)-module and J-module where J is a classes of asso-ciative algebras.By solving some matrix equations,the low-dimensional modulus of the polynomial Rota-Baxter algebra with weight 1 are characterized.