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Azumaya loci of skein algebras
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Azumaya loci of skein algebras
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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.
Forward citations
Cited by 2 Pith papers
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On the structure and representations of quantum graph algebras at roots of unity
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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Quantum cluster algebra realization for stated ${\rm SL}_n$-skein algebras and rotation-invariant bases for polygons
For polygonal surfaces, the localized stated SL_n-skein algebra equals the associated quantum cluster algebra, producing a rotation-invariant basis.
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