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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2019 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2019
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| Online Zugang: | 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 |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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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| ISSN: | 1815-0659 |