The quantization of the symplectic groupoid of the standard Podles sphere

Details The quantization of the symplectic groupoid of the standard Podles sphere The quantization of the symplectic groupoid of the standard Podles sphere

2010-04-19

arxiv.org/abs/1004.3163v2

Mathematics

Symplectic Geometry

28 pages; corrected typos.

Scientific paper

We give an explicit form of the symplectic groupoid that integrates the semiclassical standard Podles sphere. We show that Sheu's groupoid, whose convolution C*-algebra quantizes the sphere, appears as the groupoid of the Bohr-Sommerfeld leaves of a (singular) real polarization of the symplectic groupoid. By using a complex polarization we recover the convolution algebra on the space of polarized sections. We stress the role of the modular class in the definition of the scalar product in order to get the correct quantum space.

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