Representations of Polynomial Rota-Baxter Algebras

Li Qiao; Jun Pei

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arXiv · 1709.00121

Representations of Polynomial Rota-Baxter Algebras

Li Qiao·Jun Pei

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Abstract

A Rota--Baxter operator is an algebraic abstraction of integration, which is the typical example of a weight zero Rota-Baxter operator. We show that studying the modules over the polynomial Rota--Baxter algebra $(k[x],P)$ is equivalent to studying the modules over the Jordan plane, and we generalize the direct decomposability results for the $(k[x],P)$-modules in [Iy] from algebraically closed fields of characteristic zero to fields of characteristic zero. Furthermore, we provide a classification of Rota--Baxter modules up to isomorphism based on indecomposable $k[x]$-modules.

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BibTeX RIS

Li Qiao, Jun Pei. 2017-09-01. Representations of Polynomial Rota-Baxter Algebras. https://arxiv.org/abs/1709.00121

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