Unrestricted quantum moduli algebras, II: Noetherianity and simple fraction rings at roots of $1$ - Archive ouverte HAL
Article Dans Une Revue SIGMA Année : 2024

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 $\mathfrak{g}$ are Noetherian rings and finitely generated rings over $\mc(q)$. Moreover, we show that these two properties still hold on $\mc[q,q^{-1}]$ for the integral version of the quantum graph algebra. We also study the specializations $\Ll_{0,n}^\e$ of the quantum graph algebra at a root of unity $\e$ of odd order, and show that $\Ll_{0,n}^\e$ and its invariant algebra under the quantum group $U_\e(\mathfrak{g})$ have classical fraction algebras which are central simple algebras of PI degrees that we compute.
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Dates et versions

hal-03268803 , version 1 (30-06-2023)

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Stéphane Baseilhac, Philippe Roche. Unrestricted quantum moduli algebras, II: Noetherianity and simple fraction rings at roots of $1$. SIGMA, 2024, 20, pp.047. ⟨10.3842/SIGMA.2024.047⟩. ⟨hal-03268803⟩
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