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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2024 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2024
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212260 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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.
|
|---|---|
| ISSN: | 1815-0659 |