Weinstein, Alan Noncommutative geometry and geometric quantization. (English) Zbl 0756.58022 Symplectic geometry and mathematical physics, Proc. Colloq., Aix-en- Provence/ Fr. 1990, Prog. Math. 99, 446-461 (1991). [For the entire collection see Zbl 0741.00086.]The paper contains an exposition of a program initiated separately by the author, M. Karasev and S. Zakrewski. The geometric quantization of objects called symplectic groupoids is suggested as a means for relating the symplectic and Poisson manifolds of classical mechanics to noncommutative algebras. These algebras are of fundamental importance in quantum mechanics. They have also become of increasing interest because of their applications to geometry and to certain Hopf algebras called quantum groups. Reviewer: V.G.Angelov (Sofia) Cited in 3 ReviewsCited in 7 Documents MSC: 53D50 Geometric quantization 46L85 Noncommutative topology 46L87 Noncommutative differential geometry 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory Keywords:geometric quantization; noncommutative geometry; symplectic groupoids Citations:Zbl 0741.00086 PDFBibTeX XMLCite \textit{A. Weinstein}, Prog. Math. 99, 446--461 (1991; Zbl 0756.58022)