# 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} }

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…

## 73 Citations

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We investigate a quantization problem which asks for the construction of an algebra for relative elliptic problems of pseudodifferential type associated to smooth embeddings. Specifically, we study…

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