Unrestricted quantum moduli algebras, II: noetherianity and simple fraction rings at roots of 1

Stéphane Baseilhac (1) , Philippe Roche

1 IMAG - Institut Montpelliérain Alexander Grothendieck

We prove that the unrestricted quantum moduli algebra of a punctured sphere and complex simple Lie algebra $\mathfrak{g}$ is a finitely generated ring and a Noetherian ring, and that its specialization at a root of unity of odd order $l$, coprime to $3$ if $\mathfrak{g}$ has type $G_2$, embeds in a natural way in a maximal order of a central simple algebra of PI degree $l^{(n-1)N-m}$, where $N$ is the number of positive roots of $\mathfrak{g}$, $m$ its rank, and $n+1\geq 3$ the number of punctures.

Mots clés: quantum groups; invariant theory; TQFT

Domaines: Algèbres quantiques [math.QA]

Stéphane Baseilhac, Philippe Roche. Unrestricted quantum moduli algebras, II: noetherianity and simple fraction rings at roots of 1. 2021. ⟨hal-03265204v2⟩