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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