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arXiv · 2412.07158

Algebra, group, and Hopf Rota-Baxter operators

Valeriy G. Bardakov·Igor M. Nikonov·Viktor N. Zhelaybin
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Abstract

We know definition of Rota--Baxter operators on different algebraic systems. For examples, on groups, on algebras, on Hopf algebras. On some algebraic systems it is possible to define different types of Rota--Baxter operators. For example, on group algebra it is possible to define Rota--Baxter operator as on associative algebra, group Rota--Baxter operator and Rota--Baxter operator as on a Hopf algebra. We are investigating the following question: What are connections between these operators? We are studying these questions for the Sweedler algebra $H_4$, that is 4-dimension non--cocommutative Hopf algebra.

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Valeriy G. Bardakov, Igor M. Nikonov, Viktor N. Zhelaybin. 2024-12-10. Algebra, group, and Hopf Rota-Baxter operators. https://arxiv.org/abs/2412.07158

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