A groupoid approach to quantization

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Publication details

JournalJ. Symplectic Geom.
DatePublished - Mar 2008
Issue number1
Volume6
Number of pages64
Pages (from-to)61-125
Original languageEnglish

Abstract

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.

    Research areas

  • Mathematical Physics

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