Unrestricted quantum moduli algebras, II: noetherianity and simple fraction rings at roots of 1
Résumé
We prove that the quantum graph algebra and the quantum moduli algebra associated to a punctured sphere and complex semisimple Lie algebra g are Noetherian rings and finitely generated rings over C(q). Moreover, we show that these two properties still hold on C[q,q−1] for the integral version of the quantum graph algebra. We also study the specializations Lϵ0,n of the quantum graph algebra at a root of unity ϵ of odd order, and show that Lϵ0,n and its invariant algebra under the quantum group Uϵ(g) have classical fraction algebras which are central simple algebras of PI degrees that we compute.
Domaines
Algèbres quantiques [math.QA]Origine | Fichiers produits par l'(les) auteur(s) |
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