Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras
We construct a separable Frobenius monoidal functor from 𝒵(Vectω|ᴴ𝐻) to 𝒵(Vectω𝐺) for any subgroup 𝐻 of 𝐺 which preserves braiding and ribbon structure. As an application, we classify rigid Frobenius algebras in 𝒵(Vectω𝐺), recovering the classification of étale algebras in these categories by Davydo...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212009 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras. Samuel Hannah, Robert Laugwitz and Ana Ros Camacho. SIGMA 19 (2023), 075, 42 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We construct a separable Frobenius monoidal functor from 𝒵(Vectω|ᴴ𝐻) to 𝒵(Vectω𝐺) for any subgroup 𝐻 of 𝐺 which preserves braiding and ribbon structure. As an application, we classify rigid Frobenius algebras in 𝒵(Vectω𝐺), recovering the classification of étale algebras in these categories by Davydov-Simmons [J. Algebra 471 (2017), 149-175, arXiv:1603.04650] and generalizing their classification to algebraically closed fields of arbitrary characteristic. Categories of local modules over such algebras are modular tensor categories by the results of Kirillov-Ostrik [Adv. Math. 171 (2002), 183-227, arXiv:math.QA/0101219] in the semisimple case and Laugwitz-Walton [Comm. Math. Phys., to appear, arXiv:2202.08644] in the general case.
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| ISSN: | 1815-0659 |