2024/08/22 by Hiroaki Karuo, Zhihao Wang, Karuo, Hiroaki +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2408.12520
openalex publication_date 2024/08/22 · openalex created_date 2024/12/21 · openalex updated_date 2026/07/28
In the paper, we show some properties of (reduced) stated SL(n)-skein algebras related to their centers for essentially bordered pb 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 Teichmüller theory. Thanks to the Unicity theorem in [BG02, FKBL19], 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 to the representation theory of unrestricted quantum moduli algebras, and that of quantum higher cluster algebras potentially.