Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras
We construct a separable Frobenius monoidal functor from (Vectω|ᴴ) to (Vectω) for any subgroup of which preserves braiding and ribbon structure. As an application, we classify rigid Frobenius algebras in (Vectω), recovering the classification of étale algebras in these categories by Davydov-Simmon...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2023 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2023
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212009 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862546868815265792 |
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| author | Hannah, Samuel Laugwitz, Robert Ros Camacho, Ana |
| author_facet | Hannah, Samuel Laugwitz, Robert Ros Camacho, Ana |
| citation_txt | 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 |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We construct a separable Frobenius monoidal functor from (Vectω|ᴴ) to (Vectω) for any subgroup of which preserves braiding and ribbon structure. As an application, we classify rigid Frobenius algebras in (Vectω), 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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| first_indexed | 2026-03-13T01:01:38Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212009 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T01:01:38Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hannah, Samuel Laugwitz, Robert Ros Camacho, Ana 2026-01-22T09:17:03Z 2023 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 1815-0659 2020 Mathematics Subject Classification: 18M20; 18M15 arXiv:2303.04493 https://nasplib.isofts.kiev.ua/handle/123456789/212009 https://doi.org/10.3842/SIGMA.2023.075 We construct a separable Frobenius monoidal functor from (Vectω|ᴴ) to (Vectω) for any subgroup of which preserves braiding and ribbon structure. As an application, we classify rigid Frobenius algebras in (Vectω), 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. S.H. is supported by the Engineering and Physical Sciences Research Council. R.L. was supported by a Nottingham Research Fellowship. A.R.C. is supported by Cardiff University. The authors would like to especially thank the anonymous referees for their helpful comments and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras Article published earlier |
| spellingShingle | Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras Hannah, Samuel Laugwitz, Robert Ros Camacho, Ana |
| title | Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras |
| title_full | Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras |
| title_fullStr | Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras |
| title_full_unstemmed | Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras |
| title_short | Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras |
| title_sort | frobenius monoidal functors of dijkgraaf-witten categories and rigid frobenius algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212009 |
| work_keys_str_mv | AT hannahsamuel frobeniusmonoidalfunctorsofdijkgraafwittencategoriesandrigidfrobeniusalgebras AT laugwitzrobert frobeniusmonoidalfunctorsofdijkgraafwittencategoriesandrigidfrobeniusalgebras AT roscamachoana frobeniusmonoidalfunctorsofdijkgraafwittencategoriesandrigidfrobeniusalgebras |