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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2505.07343 |
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| _version_ | 1866915334925058048 |
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| author | Schauenburg, Peter |
| author_facet | Schauenburg, Peter |
| contents | In [LWY23] the authors construct the reflective center of a module category M over a braided monoidal category B. The reflective center is by construction a braided module category over B. In the case where B is the category of modules over a finite dimensional quasitriangular Hopf algebra H, acting on the category of modules over a comodule algebra, they construct a comodule algebra, the reflective algebra, whose modules are precisely the reflective center. In the construction, Majid's transmutation of H plays a crucial r{ô}le. This note centers on the transmuted H, seeking to ''explain'' its appearance through a generalization in which the acting category is no longer a module category, but admits an internal reconstructed Hopf algebra; the transmutation is a special case of this notion. As a result, in certain cases, the reflective center is simply the category of modules in M over that Hopf algebra in B. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reflective centers as categories of modules Schauenburg, Peter Category Theory In [LWY23] the authors construct the reflective center of a module category M over a braided monoidal category B. The reflective center is by construction a braided module category over B. In the case where B is the category of modules over a finite dimensional quasitriangular Hopf algebra H, acting on the category of modules over a comodule algebra, they construct a comodule algebra, the reflective algebra, whose modules are precisely the reflective center. In the construction, Majid's transmutation of H plays a crucial r{ô}le. This note centers on the transmuted H, seeking to ''explain'' its appearance through a generalization in which the acting category is no longer a module category, but admits an internal reconstructed Hopf algebra; the transmutation is a special case of this notion. As a result, in certain cases, the reflective center is simply the category of modules in M over that Hopf algebra in B. |
| title | Reflective centers as categories of modules |
| topic | Category Theory |
| url | https://arxiv.org/abs/2505.07343 |