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| Główni autorzy: | , |
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| Format: | Preprint |
| Wydane: |
2025
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| Hasła przedmiotowe: | |
| Dostęp online: | https://arxiv.org/abs/2503.08021 |
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| _version_ | 1866915405341130752 |
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| author | Lu, Daowei Wang, Dingguo |
| author_facet | Lu, Daowei Wang, Dingguo |
| contents | Let $A$ and $H$ be two cocommutative Hopf algebras such that $A$ is an $H$-bimodule Hopf algebra. Suppose that $R:A\rightarrow A$ is a linear map and $B$ is a Rota-Baxter operator of $H$. In this paper we will characterize the Rota-Baxter operators on the L-R smash product $A\natural H$ and give the necessary and sufficient conditions to make $\overline{B}$ a Rota-Baxter operator of $A\natural H$. Then we will consider the dual case, and construct a Rota-Baxter co-operator on the L-R smash coproduct $C\ltimes H$, where $C$ and $H$ are commutative Hopf algebras and $C$ is an $H$-bicomodule Hopf algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08021 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructions of Rota-Baxter operators by L-R smash products Lu, Daowei Wang, Dingguo Rings and Algebras Let $A$ and $H$ be two cocommutative Hopf algebras such that $A$ is an $H$-bimodule Hopf algebra. Suppose that $R:A\rightarrow A$ is a linear map and $B$ is a Rota-Baxter operator of $H$. In this paper we will characterize the Rota-Baxter operators on the L-R smash product $A\natural H$ and give the necessary and sufficient conditions to make $\overline{B}$ a Rota-Baxter operator of $A\natural H$. Then we will consider the dual case, and construct a Rota-Baxter co-operator on the L-R smash coproduct $C\ltimes H$, where $C$ and $H$ are commutative Hopf algebras and $C$ is an $H$-bicomodule Hopf algebra. |
| title | Constructions of Rota-Baxter operators by L-R smash products |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2503.08021 |