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- W3011796790 abstract "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." @default.
- W3011796790 created "2020-03-23" @default.
- W3011796790 creator A5077825532 @default.
- W3011796790 date "2020-03-12" @default.
- W3011796790 modified "2023-09-25" @default.
- W3011796790 title "Modules of polynomial Rota-Baxter Algebras and matrix equations" @default.
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- W3011796790 doi "https://doi.org/10.48550/arxiv.2003.05630" @default.
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