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Presentations of the Roger–Yang generalized skein algebra

Farhan Azad, Zixi Chen, Matt Dreyer, Ryan Horowitz and Han-Bom Moon

Algebraic & Geometric Topology 21 (2021) 3199–3220
Abstract

We describe presentations of the Roger–Yang generalized skein algebras for punctured spheres with an arbitrary number of punctures. This skein algebra is a quantization of the decorated Teichmüller space and generalizes the construction of the Kauffman bracket skein algebra. We also obtain a new interpretation of the homogeneous coordinate ring of the Grassmannian of planes in terms of skein theory.

Keywords
skein algebra, punctured sphere, ring presentation
Mathematical Subject Classification
Primary: 57K31
Secondary: 32G15, 57M50
References
Publication
Received: 21 July 2020
Revised: 13 December 2020
Accepted: 31 December 2020
Published: 22 November 2021
Authors
Farhan Azad
Department of Mathematics
Fordham University
New York, NY
United States
Zixi Chen
Department of Mathematics
Fordham University
New York, NY
United States
Matt Dreyer
Department of Mathematics
Cornell University
Ithaca, NY
United States
Ryan Horowitz
Department of Mathematics
New York University
New York, NY
United States
Han-Bom Moon
Department of Mathematics
Fordham University
New York, NY
United States