Unrestricted quantum moduli algebras, III: surfaces of arbitrary genus and skein algebras
Résumé
We prove that the quantum moduli algebra associated to a punctured (finite type) surface and a complex semisimple Lie algebra $\mathfrak{g}$ is a Noetherian, finitely generated ring, and that it has no non-trivial zero divisors. Moreover, we show it is isomorphic to a skein algebra of the surface, defined by means of the Reshetikhin-Turaev functor for the quantum group $U_q(\mathfrak{g})$, and which coincides with the Kauffman bracket skein algebra when $\mathfrak{g}=\mathfrak{sl}_2$.
Domaines
Mathématiques [math]| Origine | Fichiers produits par l'(les) auteur(s) |
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