Noetherian and affine properties of quantum moduli and \mathfrakg-skein algebras

2023/02/01 by Baseilhac, Stéphane, Faitg, Matthieu, Roche, Philippe
#17B37 #20G42 #57R56 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2302.00396

Abstract

We prove that the quantum moduli algebra associated to a possibly punctured compact oriented surface and a complex semisimple Lie algebra \mathfrakg is a Noetherian and finitely generated ring. If the surface has punctures, we prove also that it has no non-trivial zero divisors (i.e., it is a domain). Moreover, we show that the quantum moduli algebra is isomorphic to the skein algebra of the surface, defined by means of the Reshetikhin-Turaev functor for the quantum group U_q(\mathfrakg), and which coincides with the Kauffman bracket skein algebra when \mathfrakg=\mathfraksl₂. We obtain these results by a similar study of quantum graph algebras, which we show to be isomorphic to stated skein algebras.

Related

• Stated skein algebras of surfaces
• Degenerations Of Skein Algebras And Quantum Traces
• Quantum torus methods for Kauffman bracket skein modules
• Quantum traces and embeddings of stated skein algebras into quantum tori
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