On modules over a Hopf brace
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912980211335168 |
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| author | Rodríguez, Ramón González Pérez, Brais Ramos Raposo, Ana Belén Rodríguez |
| author_facet | Rodríguez, Ramón González Pérez, Brais Ramos Raposo, Ana Belén Rodríguez |
| contents | Let $\mathbb{H}=(H_{1},H_{2})$ be a Hopf brace in a symmetric monoidal category ${\sf C}$. In this article it is proved that the category of modules over $\mathbb{H}$ is isomorphic to the category of modules over the smash product algebra $H_{1}\sharp H_{2}$. Furthermore, the category of modules over $\mathbb{H}$ in the sense of Zhu is characterized by the condition that a certain action lies in the cocommutativity class of $H_{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22932 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On modules over a Hopf brace Rodríguez, Ramón González Pérez, Brais Ramos Raposo, Ana Belén Rodríguez Rings and Algebras 16D90, 16T05, 16S40, 18M05 Let $\mathbb{H}=(H_{1},H_{2})$ be a Hopf brace in a symmetric monoidal category ${\sf C}$. In this article it is proved that the category of modules over $\mathbb{H}$ is isomorphic to the category of modules over the smash product algebra $H_{1}\sharp H_{2}$. Furthermore, the category of modules over $\mathbb{H}$ in the sense of Zhu is characterized by the condition that a certain action lies in the cocommutativity class of $H_{2}$. |
| title | On modules over a Hopf brace |
| topic | Rings and Algebras 16D90, 16T05, 16S40, 18M05 |
| url | https://arxiv.org/abs/2603.22932 |