Representations of polynomial Rota-Baxter algebras
Representations of polynomial Rota-Baxter algebras
复制标题
多项式 Rota-Baxter 代数的表示
DOI：
10.1016/j.jpaa.2017.08.003
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发表时间：
2018
影响因子：
0.8
通讯作者：
Pei Jun
中科院分区：
文献类型：
--
作者：
Qiao Li;Pei Jun
Rota-Baxter算子是积分的代数抽象，是权重为零的Rota-Baxter算子的典型例子。证明了多项式Rota-Baxter代数（k [x]，P）上模的研究等价于Jordan平面上模的研究，并将文献[13]中关于（k [x]，P）-模的直接可分解性结果从特征零代数闭域推广到特征零域.此外，我们还基于不可分解的k [x]-模，给出了直到同构的Rota-Baxter模的分类。
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 [13] 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.