Article
| Title: | Relative Rota-Baxter operators, modules and projections (English) |
| Author: | Fernández Vilaboa, José Manuel |
| Author: | González Rodríguez, Ramón |
| Author: | Ramos Pérez, Brais |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 3 |
| Year: | 2025 |
| Pages: | 865-913 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The present article is devoted to introduce, in a braided monoidal setting, the notion of module over a relative Rota-Baxter operator. It is proved that there exists an adjunction between the category of modules associated to an invertible relative Rota-Baxter operator and the category of modules associated to a Hopf brace, which induces an equivalence by assuming certain additional hypothesis. Moreover, the notion of projection between relative Rota-Baxter operators is defined, and it is proved that those which are called ``strong'' give rise to a module according to the previous definition in the cocommutative setting. (English) |
| Keyword: | braided monoidal category |
| Keyword: | Hopf algebra |
| Keyword: | Hopf brace |
| Keyword: | relative Rota-Baxter operator |
| MSC: | 16T05 |
| MSC: | 17B38 |
| MSC: | 18M05 |
| DOI: | 10.21136/CMJ.2025.0467-24 |
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| Date available: | 2025-09-19T11:56:09Z |
| Last updated: | 2025-09-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153057 |
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