1. Center of stated SL($n$)-skein algebras
- Author
-
Karuo, Hiroaki and Wang, Zhihao
- Subjects
Mathematics - Quantum Algebra ,Mathematics - Geometric Topology ,Mathematics - Representation Theory - Abstract
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 Teichm\"uller 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., Comment: 70 pages, 12 figures
- Published
- 2024