Modular Group Representations in Combinatorial Quantization with Non-Semisimple Hopf Algebras
Let Σg,n be a compact oriented surface of genus g with n open disks removed. The algebra Lg,n(H) was introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche and is a combinatorial quantization of the moduli space of flat connections on Σg,n. Here we focus on the two building blocks L₀,₁(H) and L...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2019 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210311 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Modular Group Representations in Combinatorial Quantization with Non-Semisimple Hopf Algebras / M. Faitg // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 39 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862709525194211328 |
|---|---|
| author | Faitg, M. |
| author_facet | Faitg, M. |
| citation_txt | Modular Group Representations in Combinatorial Quantization with Non-Semisimple Hopf Algebras / M. Faitg // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 39 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Let Σg,n be a compact oriented surface of genus g with n open disks removed. The algebra Lg,n(H) was introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche and is a combinatorial quantization of the moduli space of flat connections on Σg,n. Here we focus on the two building blocks L₀,₁(H) and L₁,₀(H) under the assumption that the gauge Hopf algebra H is finite-dimensional, factorizable, and ribbon, but not necessarily semisimple. We construct a projective representation of SL₂(Z), the mapping class group of the torus, based on L₁,₀(H), and we study it explicitly for H = Ūq(sl(2)). We also show that it is equivalent to the representation constructed by Lyubashenko and Majid.
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| first_indexed | 2025-12-07T21:25:06Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210311 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:25:06Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Faitg, M. 2025-12-05T09:32:54Z 2019 Modular Group Representations in Combinatorial Quantization with Non-Semisimple Hopf Algebras / M. Faitg // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 39 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 16T05; 81R05 arXiv: 1805.00924 https://nasplib.isofts.kiev.ua/handle/123456789/210311 https://doi.org/10.3842/SIGMA.2019.077 Let Σg,n be a compact oriented surface of genus g with n open disks removed. The algebra Lg,n(H) was introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche and is a combinatorial quantization of the moduli space of flat connections on Σg,n. Here we focus on the two building blocks L₀,₁(H) and L₁,₀(H) under the assumption that the gauge Hopf algebra H is finite-dimensional, factorizable, and ribbon, but not necessarily semisimple. We construct a projective representation of SL₂(Z), the mapping class group of the torus, based on L₁,₀(H), and we study it explicitly for H = Ūq(sl(2)). We also show that it is equivalent to the representation constructed by Lyubashenko and Majid. I am grateful to my advisors, Stéphane Baseilhac and Philippe Roche, for their regular support and their useful remarks. I thank the referees for carefully reading the manuscript and for many valuable comments, which improved the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Modular Group Representations in Combinatorial Quantization with Non-Semisimple Hopf Algebras Article published earlier |
| spellingShingle | Modular Group Representations in Combinatorial Quantization with Non-Semisimple Hopf Algebras Faitg, M. |
| title | Modular Group Representations in Combinatorial Quantization with Non-Semisimple Hopf Algebras |
| title_full | Modular Group Representations in Combinatorial Quantization with Non-Semisimple Hopf Algebras |
| title_fullStr | Modular Group Representations in Combinatorial Quantization with Non-Semisimple Hopf Algebras |
| title_full_unstemmed | Modular Group Representations in Combinatorial Quantization with Non-Semisimple Hopf Algebras |
| title_short | Modular Group Representations in Combinatorial Quantization with Non-Semisimple Hopf Algebras |
| title_sort | modular group representations in combinatorial quantization with non-semisimple hopf algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210311 |
| work_keys_str_mv | AT faitgm modulargrouprepresentationsincombinatorialquantizationwithnonsemisimplehopfalgebras |