Relative Rota-Baxter operators, modules and projections
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915332218683392 |
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| author | Vilaboa, José Manuel Fernández Rodríguez, Ramón González Pérez, Brais Ramos |
| author_facet | Vilaboa, José Manuel Fernández Rodríguez, Ramón González Pérez, Brais Ramos |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_12782 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative Rota-Baxter operators, modules and projections Vilaboa, José Manuel Fernández Rodríguez, Ramón González Pérez, Brais Ramos Rings and Algebras 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. |
| title | Relative Rota-Baxter operators, modules and projections |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2406.12782 |