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- Title
- CENTER OF STATED SL(n)-SKEIN ALGEBRAS
- KIAS Author
- Wang, Zhihao
- Journal
- TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2026
- Archive
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- Abstract
- In the paper, we show some properties of (reduced) stated SL(n)-skein algebras related to their centers for essentially bordered punctured bordered surfaces, especially their centers, finitely generation over their centers, and their PI-degrees. The proofs are based on the quantum trace maps, embeddings of (reduced) stated SL(n)-skein algebras into quantum tori appearing in higher Teichmuller theory. Thanks to the Unicity theorem by Brown and Goodearl [Lectures on algebraic quantum groups, Birkhauser Verlag, Basel, 2002] and Frohman, Kania-Bartoszynska, and Le [Invent. Math. 215 (2019), pp. 609-650], we can understand the representation theory of (reduced) stated SL(n)-skein algebras. Moreover, the applications are beyond low-dimensional topology. For example, we can access the representation theory of unrestricted quantum moduli algebras, and that of quantum higher cluster algebras potentially.
