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Azumaya loci of skein algebras

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arxiv 2211.13700 v4 pith:VLLA5A4G submitted 2022-11-24 math.QA

Hiroaki Karuo , Julien Korinman This is my paper · ORCID
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keywords skeinalgebrasazumayaclosedlocisurfacesalternativeapplications
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We compute the Azumaya loci of Kauffman-bracket skein algebras of closed surfaces at odd roots of unity and provide partial results for open surfaces as well. As applications, we give an alternative definition of the projective representations of the Torelli groups derived from non-semisimple TQFTs and we strengthen a result by Frohman-Kania Bartoszynska-L\^e about the dimensions of some quotients of the skein modules of closed 3-manifolds.

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Cited by 1 Pith paper

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  1. On the structure and representations of quantum graph algebras at roots of unity

    math.QA 2026-01 accept novelty 7.0 of 10

    Root-of-unity quantum graph algebras have irreducible representations of maximal dimension l^{g·dim(g)+n·N}, and their small-quantum-group invariants have maximal dimension l^{g·dim(g)+N(n−1)−m}, with centers describe...

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