Representations of the Kauffman bracket skein algebra of the punctured torus
Volume 225 / 2014
Fundamenta Mathematicae 225 (2014), 45-55
MSC: 81S10, 81R50, 57R56, 81T45, 57M25.
DOI: 10.4064/fm225-1-3
Abstract
We describe the action of the Kauffman bracket skein algebra on some vector spaces that arise as relative Kauffman bracket skein modules of tangles in the punctured torus. We show how this action determines the Reshetikhin–Turaev representation of the punctured torus. We rephrase our results to describe the quantum group quantization of the moduli space of flat ${\rm SU}(2)$-connections on the punctured torus with fixed trace of the holonomy around the boundary.
