Research output: Contribution to journal › Article

Journal | J. Symplectic Geom. |
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Date | Published - Mar 2008 |

Issue number | 1 |

Volume | 6 |

Number of pages | 64 |

Pages (from-to) | 61-125 |

Original language | English |

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.

- Mathematical Physics

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