|XXIX Workshop on Geometric Methods in Physics
Geometric quantization for the standard Podles sphere
The standard Podles sphere has become a test case for various quantization procedures. We will show how to apply geometric quantization to the symplectic groupoid integrating such Poisson structure; the emphasis will be put on quantizing the modular class; this will show relations between its algebraic quantization, as van den Bergh automorphism, and its analytic quantization as Tomita-Takesaki operator. We will also show how Sheu's groupoid C^* algebra can be recovered from a BS-type condition.