Modules of Non-unital Polynomial Rota-Baxter Algebras

被引：0
作者：
Xiaomin Tang
Na Liu
机构：
[1] Heilongjiang University,School of Mathematical Science
来源：
Algebras and Representation Theory | 2023年 / 26卷
关键词：
Module; Rota-Baxter algebra; Non-unital Rota-Baxter algebra; Matrix equation; 16W99; 16P70; 16G99;
D O I：
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学科分类号：
摘要：
In this paper, we study the free commutative non-unital Rota-Baxter algebra which is the algebra of polynomials in one variable without constant term with Rota-Baxter operators of nonzero weight. The main result shows that every module over this Rota-Baxter algebra is equivalent to the modules over a noncommutative algebra generated by two indeterminates with a generation relationship. Furthermore, we study their irreducible and indecomposable modules. Finally we provide the classification of modules of nonzero weight through solution to some matrix equations.
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页码：1295 / 1318
页数：23
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