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March 2008 A groupoid approach to quantization
Eli Hawkins
J. Symplectic Geom. 6(1): 61-125 (March 2008).

Abstract

Many interesting $C∗$-algebras can be viewed as quantizations of Poisson manifolds. I propose that a Poisson manifold may be quantized by a twisted polarized convolution $C∗$-algebra of a symplectic groupoid. Toward this end, I define polarizations for Lie groupoids and sketch the construction of this algebra. A large number of examples show that this idea unifies previous geometric constructions, including geometric quantization of symplectic manifolds and the $C∗$-algebra of a Lie groupoid. I sketch a few new examples, including twisted groupoid $C∗$-algebras as quantizations of bundle affine Poisson structures.

Citation

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Eli Hawkins. "A groupoid approach to quantization." J. Symplectic Geom. 6 (1) 61 - 125, March 2008.

Information

Published: March 2008
First available in Project Euclid: 2 July 2008

zbMATH: 1154.46041
MathSciNet: MR2417440

Subjects:
Primary: 46L65
Secondary: 22A22 , 53D17 , 53D50

Rights: Copyright © 2008 International Press of Boston

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Vol.6 • No. 1 • March 2008
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