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 g is a finitely generated ring and a Noetherian ring, and that specializations at roots of unity of odd order l embed in a natural way in a central simple algebra of PI degree l^{(n−1)N −m}, where N is the number of positive roots of g, m its rank, and n + 1 ≥ 3 the number of punctures.

Mots clés: quantum groups; invariant theory; TQFT AMS subject classification 2020: 16R30; 17B37; 20G42; 57R56 Contents 40 6.2. Regular action on O 43 References 44

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-03265204v1⟩