Local cohomology of the algebra of \(C^\infty\) functions on a connected manifold. (English) Zbl 0453.58026

Cahen, M.; Gutt, S.; De Wilde, Marc

Lett. Math. Phys. 4, 157-167 (1980).

MSC:

58H99	Pseudogroups, differentiable groupoids and general structures on manifolds
58H15	Deformations of general structures on manifolds
58H10	Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)
58J99	Partial differential equations on manifolds; differential operators
53D50	Geometric quantization

Keywords:

local and differentiable Hochschild cohomology; local Chevalley cohomology; differentiable Chevalley cohomology; deformation of classical mechanics; deformations of the Poisson bracket of functions on phase space; multilinear local operator acting on the space of functions on a manifold; differentiable operator

References:

[1]	Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A. and Sternheimer D., ?Deformation theory and quantization?, Ann. Phys. 111, 61, 111 (1978). · Zbl 0377.53024
[2]	Gutt, S., ?2ème et 3ème espaces de cohomologie différentiable de l’algèbre de Lie de Poisson d’une variété symplectique?, Preprint. · Zbl 0476.53021
[3]	Lichnerowicz, A., ?Cohomologie 1-différentiable des algèbres de Lie attachées à une variété symplectique ou de contact?, J. Math. Pures et Appl. 53, 459-484 (1974).
[4]	Peetre, J., ?Une caractérisation abstraite des opérateurs différentiels?, Math. Scandinavica, 8, 116-120.
[5]	Shiga, Journ. Math. Soc. Japan, V26 (2), 324-361 (1974). · Zbl 0273.58002
[6]	Vey J., ?Déformation du crochet de Poisson sur une variété symplectique?, Comment. Math. Helvet. 50, 421 (1975). · Zbl 0351.53029