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Star products on compact pre-quantizable symplectic manifolds. (English) Zbl 0842.58041
Author’s summary: The purpose of this letter is to point out the relevance of some relatively ancient work of Boutet de Monvel and myself to recent developments in the theory of star products and deformation quantization (…), on the existence of star products with nice geometric properties.

MSC:
53D50 Geometric quantization
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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[1] Boutet-de-Monvel, L.: On the index of Toeplitz operators of several complex variables,Invent. Math. 50, 249-272 (1979). · Zbl 0398.47018 · doi:10.1007/BF01410080
[2] Boutet-de-Monvel, L. and Guillemin, V.:The Spectral Theory of Toeplitz Operators, Ann. of Math. Studies 99, Princeton Univ. Press, Princeton, NJ; 1981. · Zbl 0469.47021
[3] Connes, A., Flato, M. and Sternheimer, D.: Closed star products and cyclic cohomology,Lett. Math. Phys. 24, 1-12 (1992). · Zbl 0767.55005 · doi:10.1007/BF00429997
[4] Fedosov, B. V.: A simple geometrical construction of deformation quantization,J. Differential Geom. (to appear). · Zbl 0812.53034
[5] Fedosov, B. V.: Proof of the index theorem for deformation quantization, Max-Planck-Gesellshaft zur Forderung der Wissenschaft, Bonn (1994).
[6] Kostant, B.: Quantization and unitary representations, inLectures in Modern Analysis and Applications, Lecture Notes in Math. 170, Springer-Verlag, New York, 1970, 87-208.
[7] Lecomte, P. B. and De Wilde, M.: Existence of star products and formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds,Lett. Math. Phys. 7, 487-496 (1983). · Zbl 0526.58023 · doi:10.1007/BF00402248
[8] Omori, H., Maede, Y., and Yoshioka, A.: Existence of a closed star-product,Lett. Math. Phys. 26, 285-294 (1992). · Zbl 0771.58017 · doi:10.1007/BF00420238
[9] Souriau, J.-M,Structures des systémès dynamiques, Dunod, Paris, 1970. · Zbl 0186.58001
[10] Weinstein, A.,Séminaire Bourbaki, Paris, June 1994.
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