The quantization of the symplectic groupoid of the standard Podles sphere

JOURNAL OF GEOMETRY AND PHYSICS

卷:62

Article

Bonechi, F.^1,2  Ciccoli, N.³  Staffolani, N.^1,2  Tarlini, M.^1,2 

[1] Univ Florence, Ist Nazl Fis Nucl, Sez Firenze, I-50121 Florence, Italy

[2] Univ Florence, Dipartimento Fis, I-50121 Florence, Italy

[3] Univ Perugia, Dipartimento Matemat, I-06100 Perugia, Italy

关键词: Poisson geometry;    Symplectic groupoids;    Groupoid C*-algebras;    Geometric quantization;   

DOI  :  10.1016/j.geomphys.2012.04.001

来源: Elsevier

【 摘 要 】

We give an explicit form of the symplectic groupoid g(S-2, pi) that integrates the semiclassical standard Podles sphere (S-2. pi). We show that Sheu's groupoid g(S), whose convolution C*-algebra quantizes the sphere, appears as the groupoid of the Bohr-Sommerfeld leaves of a (singular) real polarization of g(S-2. pi). 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. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

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