Journal of Symplectic Geometry
- J. Symplectic Geom.
- Volume 6, Number 1 (2008), 61-125.
A groupoid approach to quantization
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.
J. Symplectic Geom., Volume 6, Number 1 (2008), 61-125.
First available in Project Euclid: 2 July 2008
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46L65: Quantizations, deformations
Secondary: 53D17: Poisson manifolds; Poisson groupoids and algebroids 22A22: Topological groupoids (including differentiable and Lie groupoids) [See also 58H05] 53D50: Geometric quantization
Hawkins, Eli. A groupoid approach to quantization. J. Symplectic Geom. 6 (2008), no. 1, 61--125. https://projecteuclid.org/euclid.jsg/1215032733