A Groupoid Approach to Quantization

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dc.creatorHawkins, Eli
dc.date2006-12-13
dc.date2007-09-18
dc.date.accessioned2026-07-07T08:30:12Z
dc.date.available2026-07-07T08:30:12Z
dc.descriptionMany 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.
dc.description60 pages. V3: Minor corrections including Def 4.4. Added details in sections 6.1 and 8.2. Additional references. Some signs changed
dc.identifierhttps://arxiv.org/abs/math/0612363
dc.identifierhttp://arxiv.org/abs/math/0612363
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138183
dc.subjectSymplectic Geometry
dc.subjectMathematical Physics
dc.subjectOperator Algebras
dc.subject46L65; 53D17; 22A22, 53D50
dc.titleA Groupoid Approach to Quantization
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