Presentations of the Roger-Yang generalized skein algebra
Farhan Azad, Zixi Chen, Matt Dreyer, Ryan Horowitz, Han-Bom Moon
TL;DR
This paper provides presentations of the Roger-Yang generalized skein algebra for punctured spheres, connecting it to decorated Teichmuller space and offering a new skein-theoretic interpretation of Grassmannian coordinate rings.
Contribution
It introduces explicit presentations of the generalized skein algebra for punctured spheres and links skein theory to Grassmannian coordinate rings.
Findings
Presentations of the skein algebra for punctured spheres are established.
A new skein-theoretic interpretation of Grassmannian coordinate rings is provided.
The work generalizes the Kauffman bracket skein algebra to a broader setting.
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 Teichmuller space and generalizes the construction of the Kauffman bracket skein algebra. In this paper, we also obtain a new interpretation of the homogeneous coordinate ring of the Grassmannian of planes in terms of skein theory.
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