# A Groupoid Approach to Quantization

```@article{Hawkins2006AGA,
title={A Groupoid Approach to Quantization},
author={Eli Hawkins},
journal={Journal of Symplectic Geometry},
year={2006},
volume={6},
pages={61-125}
}```
• E. Hawkins
• Published 13 December 2006
• Mathematics
• Journal of Symplectic Geometry
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…
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