论文标题
多项式Rota-Baxter代数和基质方程的模块
Modules of polynomial Rota-Baxter Algebras and matrix equations
论文作者
论文摘要
多项式代数$ r = {\ bf k} [x] $上的所有rota-baxter代数结构是众所周知的。我们研究了多项式旋转式代数$（\ bfk [x]，p）$或$（x {x {\ bf k} [x]，p）$ nonzero的有限尺寸模块，因为某些重量零病例的重量为零。主要结果表明，多项式rota-baxter代数$（\ bfk [x]，p），p）$或$（x {x {\ bf k} [x]，p）$等于平面上的模块$ {\ bf k} k} \ langle x，y \ rangle $。此外，我们通过求解某些矩阵方程的求解，提供重量非零的多项式旋转式代数的模块的分类。
The all Rota-Baxter algebra structures on the polynomial algebra $R={\bf k}[x]$ are well known. We study the finite dimensional modules of polynomial Rota-Baxter algebras $(\bfk[x],P)$ or $(x {\bf k} [x],P)$ of weight nonzero since some cases of weight zero have been studied. The main result shows that every module over the polynomial Rota-Baxter algebra $(\bfk[x],P)$ or $(x {\bf k} [x],P)$ is equivalent to the modules over a plane ${\bf k}\langle x,y \rangle/ I$ where $I$ is some ideal of free algebra ${\bf k}\langle x,y \rangle$. Furthermore, we provide the classification of modules of polynomial Rota-Baxter algebras of weight nonzero through solution to some matrix equation.
