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De Wilde, Marc; Lecomte, Pierre B. A.

Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds. (English) Zbl 0526.58023

Lett. Math. Phys. 7, 487-496 (1983).
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Cited in 9 Reviews
Cited in 139 Documents

MSC:

53D55 Deformation quantization, star products
53D17 Poisson manifolds; Poisson groupoids and algebroids
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
58A12 de Rham theory in global analysis

Keywords:

Weyl transformation; Poisson bracket; Moyal product; Planck constant; De Rham cohomology

Citations:

Zbl 0465.53024; Zbl 0031.33601; Zbl 0377.53024; Zbl 0377.53025; Zbl 0351.53029; Zbl 0471.58034; Zbl 0514.53031
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Full Text: DOI

References:

[1] ArnalD., CortetJ.C., FlatoM., and SternheimerD., ?Star-Products: Quantization and Representation Without Operators?, in E.Tirapegui (ed.), Field Theory Quantization and Statistical Physics, Reidel, Dordrecht, 1981, pp. 85-111.
[2] CahenM. and GuttS., Lett. Math. Phys. 6, 395-404 (1982). · Zbl 0522.58018 · doi:10.1007/BF00419321
[3] De Wilde, M., Gutt, S., and Lecomte, P., ?A propos des deuxième et troisième espaces de cohomologie de l’algèbre de Lie de Poisson d’une variété symplectique?, Ann. Inst. Poincaré, to appear. · Zbl 0547.53024
[4] DeWildeM. and LecomteP., Lett. Math. Phys. 7, 235-241 (1983). · Zbl 0514.53031 · doi:10.1007/BF00400439
[5] De Wilde, M. and Lecomte, P., ?Existence of Star-Products on Exact Symplectic Manifolds?, to appear. · Zbl 0536.58038
[6] FlatoM., and SternheimerD. ?Deformation of Poisson Brackets?, in J.Wolf et al. (eds.), Harmonic Analysis and Representation of Semi Simple Lie Group, Reidel, Dordrecht, 1980, pp. 385-448.
[7] GuttS., Ann. Inst. Poincaré 33, 1-31 (1981).
[8] LichnerowiczA., Ann. Inst. Fourier 32, 157-209 (1982).
[9] MoyalJ.E., Proc. Cambridge Phil. Soc. 45, 99-124 (1949). · doi:10.1017/S0305004100000487
[10] VeyJ.. Comm. Math. Helv. 50, 421-454 (1975). · Zbl 0351.53029 · doi:10.1007/BF02565761
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