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- Title
- On Frobenius algebras obtained from stated skein algebras
- KIAS Author
- Wang, Zhihao
- Journal
- TOPOLOGY AND ITS APPLICATIONS, 2026
- Archive
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- Abstract
- For any finite dimensional algebra A over a field F, there is an F-linear map "TraceF ", called the Trace function, from A to F, defined by TraceF(a) = Trace(La), where La is an F-linear map from A to A defined by sending b to ab. When the quantum parameter q 1 2 is a root of unity of odd order and the punctured bordered surface has nonempty boundary, we prove the Trace function makes the fraction ring of the stated skein algebra (that is the localization over all nonzero elements) into 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 give explicit formulas for the Trace functions of the fraction ring of the stated skein algebra over these two fields. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
