On Frobenius algebras obtained from stated skein algebras

2023/10/19 by Wang, Zhihao
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2310.13116

Abstract

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 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.

Related

• Finiteness and dimension of stated skein modules over Frobenius
• Noetherian and affine properties of quantum moduli and \mathfrakg-skein algebras
• Degenerations Of Skein Algebras And Quantum Traces
• Frobenius algebras and skein modules of surfaces in 3-manifolds
• The Unicity Theorem and the center of the \rm SL₃-skein algebra