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Center of the stated skein algebra

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arxiv 2309.14713 v1 pith:W2NTEX3C submitted 2023-09-26 math.QA math.GT

Center of the stated skein algebra

Tao Yu This is my paper
classification math.QA math.GT
keywords algebracenterskeinstatedquantumbracketcalculatedescription
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The stated skein algebra is a generalization of the Kauffman bracket skein algebra introduced in the study of quantum trace maps. When the quantum parameter is a root of unity, the stated skein algebra has a big center and is finitely generated as a module over the center. We give the center a simple description and calculate the dimension over center of the stated skein algebra.

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  1. Quantum cluster algebra realization for stated ${\rm SL}_n$-skein algebras and rotation-invariant bases for polygons

    math.QA 2026-05 unverdicted novelty 6.0

    For polygonal surfaces, the localized stated SL_n-skein algebra equals the associated quantum cluster algebra, producing a rotation-invariant basis.