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• W2023686765 abstract "Alternative titles of this paper would have been ``Index theory without index'' or ``The Baum–Connes conjecture without Baum.'' In 1989, Rieffel introduced an analytic version of deformation quantization based on the use of continuous fields of C * -algebras. We review how a wide variety of examples of such quantizations can be understood on the basis of a single lemma involving amenable groupoids. These include Weyl–Moyal quantization on manifolds, C * -algebras of Lie groups and Lie groupoids, and the E-theoretic version of the Baum–Connes conjecture for smooth groupoids as described by Connes in his book Noncommutative Geometry. Concerning the latter, we use a different semidirect product construction from Connes. This enables one to formulate the Baum–Connes conjecture in terms of twisted Weyl–Moyal quantization. The underlying mechanical system is a noncommutative desingularization of a stratified Poisson space, and the Baum–Connes Conjecture actually suggests a strategy for quantizing such singular spaces." @default.
• W2023686765 created "2016-06-24" @default.
• W2023686765 creator A5060266645 @default.
• W2023686765 date "2003-06-01" @default.
• W2023686765 modified "2023-09-25" @default.
• W2023686765 title "Deformation Quantization and the Baum–Connes Conjecture" @default.
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• W2023686765 doi "https://doi.org/10.1007/s00220-003-0838-0" @default.
• W2023686765 hasPublicationYear "2003" @default.
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