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February 22, 2026Transactions of the American Mathematical Society0 citations

Azumaya loci of skein algebras

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HKHiroaki KaruoJKJulien Korinman

Key Points

  • This research aims to compute the azumaya loci of skein algebras, especially focusing on closed surfaces at odd roots of unity.
  • Computed azumaya loci for Kauffman-bracket skein algebras of closed surfaces.
  • Explored partial results for open surfaces.
  • Derived alternative definitions of projective representations of Torelli groups from non-semisimple TQFTs.
  • Strengthened existing results regarding dimensions of skein modules of closed 3-manifolds.
  • Provided explicit computations of azumaya loci for closed surfaces.
  • Offered new definitions that relate to projective representations of Torelli groups.
  • Enhanced understanding of dimensions of skein module quotients, building on prior work by Frohman-Kania Bartoszynska-Lê.

Abstract

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-Lê about the dimensions of some quotients of the skein modules of closed 3-manifolds.

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Cite This Study

Karuo et al. (2026) studied this question.

synapsesocial.com/papers/699a9e00482488d673cd44f5https://doi.org/10.1090/tran/9516
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