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Modules of Non-unital Polynomial Rota-Baxter Algebras

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Abstract

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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Acknowledgments

We would like to thank the referee for invaluable comments and suggestions. This work is supported in part by NNSFC (No. 11771069), NSF of Heilongjiang Province (No. LH2020A020) and the fund of Heilongjiang Provincial Laboratory of the Theory and Computation of Complex Systems.

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  1. School of Mathematical Science, Heilongjiang University, Harbin, 150080, People’s Republic of China

    **aomin Tang & Na Liu

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  1. **aomin Tang
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  2. Na Liu
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Correspondence to **aomin Tang.

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Tang, X., Liu, N. Modules of Non-unital Polynomial Rota-Baxter Algebras. Algebr Represent Theor 26, 1295–1318 (2023). https://doi.org/10.1007/s10468-022-10134-5

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