Presentations of the Roger–Yang generalized skein algebra

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.