About Hopf braces and crossed products
The present article represents a step forward in the study of the following problem: If A = (A1, A2) and H = (H1, H2) are Hopf braces in a symmetric monoidal category C such that (A1, H1) and (A2, H2) are matched pairs of Hopf algebras, then we want to know under what conditions the pair (A1 ▷◁ H1,...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2025 |
| Country: | España |
| Institution: | Universidad de Santiago de Compostela (USC) |
| Repository: | Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela |
| Language: | English |
| OAI Identifier: | oai:minerva.usc.gal:10347/45209 |
| Online Access: | https://hdl.handle.net/10347/45209 |
| Access Level: | Embargoed access |
| Keyword: | Symmetric monoidal category Hopf algebra Matched pair Bicrossed product Smash product Hopf brace Drinfeld’s Double |
| Summary: | The present article represents a step forward in the study of the following problem: If A = (A1, A2) and H = (H1, H2) are Hopf braces in a symmetric monoidal category C such that (A1, H1) and (A2, H2) are matched pairs of Hopf algebras, then we want to know under what conditions the pair (A1 ▷◁ H1, A2 ▷◁ H2) constitutes a new Hopf brace. We find such conditions for the pairs (A1 ⊗ H1, A2 ▷◁ H2) and (A1 ▷◁ H1, A2♯H2) to be Hopf braces, which are particular situations of the general problem described above, analyzing when these are cocommutative, leading to solutions to the Quantum Yang-Baxter equation. These results are applied to study when the Drinfeld’s Double gives rise to a Hopf brace. |
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