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On Frobenius algebras obtained from stated skein algebras
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On Frobenius algebras obtained from stated skein algebras
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When the quantum parameter $q^{\frac{1}{2}}$ is a root of unity of odd order and the punctured bordered surface has nonempty boundary, we prove the fraction ring of the stated skein algebra (that is the localization over all nonzero elements) is a symmetric Frobenius algebra over both the field of fractions of the image of the Frobenius map and the field of fractions of the center of the stated skein algebra. We also calculate Traces of the fraction ring of the stated skein algebra over these two fields.
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Cited by 1 Pith paper
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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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