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arXiv 2003.05630math.RT
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多项式Rota-Baxter代数与矩阵方程的模

Modules of polynomial Rota-Baxter Algebras and matrix equations

Xiaomin Tang

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16 pages
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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。本文研究了权非零的多项式Rota-Baxter代数$(\bfk[x],P)$或$(x {\bf k} [x],P)$的有限维模，因为权为零的情形已经被研究过.主要结果表明：多项式Rota-Baxter代数$(\bfk[x],P)$或$(x {\bf k} [x],P)$上的每个模都等价于平面${\bf k}\langle x,y \rangle/ I$上的模，其中$I$是自由代数${\bf k}\langle x,y \rangle$的某个理想.此外，通过对矩阵方程的求解，给出了权非零的多项式Rota-Baxter代数的模的分类.

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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