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arXiv · 1407.5306

Rota-Baxter operators on the polynomial algebras, integration and averaging operators

Li Guo·Markus Rosenkranz·Shanghua Zheng
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Abstract

Rota-Baxter operators are an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota-Baxter operators and integrals in the case of the polynomial algebra $\mathbf{k}[x]$. We consider two classes of Rota-Baxter operators, monomial ones and injective ones. For the first class, we apply averaging operators to determine monomial Rota-Baxter operators. For the second class, we make use of the double product on Rota-Baxter algebras.

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Li Guo, Markus Rosenkranz, Shanghua Zheng. 2014-07-20. Rota-Baxter operators on the polynomial algebras, integration and averaging operators. https://doi.org/10.2140/pjm.2015.275.481

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