Braided categories of bimodules from stated skein TQFTs
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918371668262912 |
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| author | Costantino, Francesco Faitg, Matthieu |
| author_facet | Costantino, Francesco Faitg, Matthieu |
| contents | For each braided category $\mathcal{C}$ we show that, under mild hypotheses, there is an associated category of "half braided algebras" and their bimodules internal to $\mathcal{C}$ which is not only monoidal but even braided and balanced. We use this in the case where $\mathcal{C}$ is the category of modules over a ribbon Hopf algebra to interpret stated skeins as a TQFT, namely a braided balanced functor from a category of cobordisms to this category of algebras and their bimodules. Although our construction works in full generality, we relate in the special case of finite-dimensional ribbon factorizable Hopf algebras the stated skein functor to the Kerler-Lyubashenko TQFT by interpreting the former as the "endomorphisms" of the latter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16909 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Braided categories of bimodules from stated skein TQFTs Costantino, Francesco Faitg, Matthieu Quantum Algebra Geometric Topology 57K16 (Primary) 16D90, 18M15 (Secondary) For each braided category $\mathcal{C}$ we show that, under mild hypotheses, there is an associated category of "half braided algebras" and their bimodules internal to $\mathcal{C}$ which is not only monoidal but even braided and balanced. We use this in the case where $\mathcal{C}$ is the category of modules over a ribbon Hopf algebra to interpret stated skeins as a TQFT, namely a braided balanced functor from a category of cobordisms to this category of algebras and their bimodules. Although our construction works in full generality, we relate in the special case of finite-dimensional ribbon factorizable Hopf algebras the stated skein functor to the Kerler-Lyubashenko TQFT by interpreting the former as the "endomorphisms" of the latter. |
| title | Braided categories of bimodules from stated skein TQFTs |
| topic | Quantum Algebra Geometric Topology 57K16 (Primary) 16D90, 18M15 (Secondary) |
| url | https://arxiv.org/abs/2505.16909 |