Generalized quantum cluster structure of reduced Lê--Roger--Yang skein algebras and their Frobenius maps
Year: 2026
Type: preprint
Abstract: We establish a generalized quantum cluster algebra structure, defined by Bai--Chen--Ding--Xu, on the reduced Lê--Roger--Yang skein algebra of every quasi-triangulable punctured surface. We define Frobenius maps for generalized quantum cluster algebras at roots of unity and use these maps, together with the cluster algebra structure, to construct Frobenius maps for the (reduced) Lê--Roger--Yang skein algebras of all punctured surfaces. As applications of the Frobenius map, we determine the centers of both the Muller--Roger--Yang skein algebras and the reduced Lê--Roger--Yang skein algebras at roots of unity, and compute their ranks as modules over their centers.
Source: arXiv (Cornell University)
Authors: Huang, Min, Wang, Zhihao
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220697072