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24 June 2024
 
  » arxiv » 2302.00396

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Unrestricted quantum moduli algebras, III: Surfaces of arbitrary genus and skein algebras
St├ęphane Baseilhac ; Matthieu Faitg ; Philippe Roche ;
Date 1 Feb 2023
AbstractWe 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 $mathfrak{g}=mathfrak{sl}_2$.
Source arXiv, 2302.00396
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