Unrestricted Quantum Moduli Algebras, II: Noetherianity and Simple Fraction Rings at Roots of 1
We prove that the quantum graph algebra and the quantum moduli algebra associated to a punctured sphere and a complex semisimple Lie algebra are Noetherian rings and finitely generated rings over ℂ(). Moreover, we show that these two properties still hold on ℂ[, ⁻¹] for the integral version of the...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212260 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Unrestricted Quantum Moduli Algebras, II: Noetherianity and Simple Fraction Rings at Roots of 1. Stéphane Baseilhac and Philippe Roche. SIGMA 20 (2024), 047, 70 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862708897113964544 |
|---|---|
| author | Baseilhac, Stéphane Roche, Philippe |
| author_facet | Baseilhac, Stéphane Roche, Philippe |
| citation_txt | Unrestricted Quantum Moduli Algebras, II: Noetherianity and Simple Fraction Rings at Roots of 1. Stéphane Baseilhac and Philippe Roche. SIGMA 20 (2024), 047, 70 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove that the quantum graph algebra and the quantum moduli algebra associated to a punctured sphere and a complex semisimple Lie algebra are Noetherian rings and finitely generated rings over ℂ(). Moreover, we show that these two properties still hold on ℂ[, ⁻¹] for the integral version of the quantum graph algebra. We also study the specializations ϵ₀,ₙ of the quantum graph algebra at a root of unity ϵ of odd order, and show that ϵ₀,ₙ and its invariant algebra under the quantum group ϵ() have classical fraction algebras which are central simple algebras of PI degrees that we compute.
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| first_indexed | 2026-03-19T07:57:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212260 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T07:57:07Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Baseilhac, Stéphane Roche, Philippe 2026-02-03T07:56:26Z 2024 Unrestricted Quantum Moduli Algebras, II: Noetherianity and Simple Fraction Rings at Roots of 1. Stéphane Baseilhac and Philippe Roche. SIGMA 20 (2024), 047, 70 pages 1815-0659 2020 Mathematics Subject Classification: 16R30; 17B37; 20G42; 57M27; 57R56; 81R50 arXiv:2106.04136 https://nasplib.isofts.kiev.ua/handle/123456789/212260 https://doi.org/10.3842/SIGMA.2024.047 We prove that the quantum graph algebra and the quantum moduli algebra associated to a punctured sphere and a complex semisimple Lie algebra are Noetherian rings and finitely generated rings over ℂ(). Moreover, we show that these two properties still hold on ℂ[, ⁻¹] for the integral version of the quantum graph algebra. We also study the specializations ϵ₀,ₙ of the quantum graph algebra at a root of unity ϵ of odd order, and show that ϵ₀,ₙ and its invariant algebra under the quantum group ϵ() have classical fraction algebras which are central simple algebras of PI degrees that we compute. We are grateful to M. Faitg for many valuable discussions on the subject, especially concerning the filtration arguments in the proof of Theorem 1.1, and the use of the partial order ⪯ in the proof of Theorem 1.1. We also thank K.A. Brown for pointing out the references [6] and [25] (see the comments before Theorem 1.2). We also thank the referees for their comments and suggestions, which greatly improved the clarity of our work. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Unrestricted Quantum Moduli Algebras, II: Noetherianity and Simple Fraction Rings at Roots of 1 Article published earlier |
| spellingShingle | Unrestricted Quantum Moduli Algebras, II: Noetherianity and Simple Fraction Rings at Roots of 1 Baseilhac, Stéphane Roche, Philippe |
| title | Unrestricted Quantum Moduli Algebras, II: Noetherianity and Simple Fraction Rings at Roots of 1 |
| title_full | Unrestricted Quantum Moduli Algebras, II: Noetherianity and Simple Fraction Rings at Roots of 1 |
| title_fullStr | Unrestricted Quantum Moduli Algebras, II: Noetherianity and Simple Fraction Rings at Roots of 1 |
| title_full_unstemmed | Unrestricted Quantum Moduli Algebras, II: Noetherianity and Simple Fraction Rings at Roots of 1 |
| title_short | Unrestricted Quantum Moduli Algebras, II: Noetherianity and Simple Fraction Rings at Roots of 1 |
| title_sort | unrestricted quantum moduli algebras, ii: noetherianity and simple fraction rings at roots of 1 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212260 |
| work_keys_str_mv | AT baseilhacstephane unrestrictedquantummodulialgebrasiinoetherianityandsimplefractionringsatrootsof1 AT rochephilippe unrestrictedquantummodulialgebrasiinoetherianityandsimplefractionringsatrootsof1 |