The quantization of the symplectic groupoid of the standard Podlès sphere
type: Item
instance of: scholarly article
title: The quantization of the symplectic groupoid of the standard Podlès sphere
zbMATH Open document ID: 1245.53063
published in: Journal of Geometry and Physics
publication date: 2012-07-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1004.3163
review text: The simplest example of quantum homogeneous space, namely the standard Podleś sphere \((\mathbb{S}^2, \pi )\), is analyzed in this paper from the point of view of geometric quantization; here \(\pi \) is the Poisson structure. More precisely, the symplectic groupoid of \((\mathbb{S}^2, \pi )\) is completely described as well as a partition of this symplectic groupoid in Lagrangian submanifolds whose Bohr-Sommerfeld leaves reproduce the Sheu groupoid. Two distinct polarizations of the symplectic groupoid are obtained; the first one is real and singular, the second being complex and recovers the convolution algebra on the space of polarized sections.
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 22A22
zbMATH DE Number: 6052803
zbMATH Keywords: Poisson geometry
zbMATH Keywords: symplectic groupoids
zbMATH Keywords: groupoid \(C^{\ast }\)-algebras
zbMATH Keywords: geometric quantization
author: Francesco Bonechi
author: N. Ciccoli
author: N. Staffolani
author: M. Tarlini
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
OpenAlex ID: W2014599394
arXiv ID: 1004.3163
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DOI: 10.1016/J.GEOMPHYS.2012.04.001
description: scientific article; zbMATH DE number 6052803