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Weyl manifolds and deformation quantization. (English) Zbl 0734.58011
This paper deals with non-commutative objects based on the Weyl algebra from a differential geometric viewpoint. The main result of this paper is the statement that over any symplectic manifold there exists a Weyl manifold. This theorem then leads to the further result that any symplectic manifold is deformation quantizable.

MSC:
46L85 Noncommutative topology
46L87 Noncommutative differential geometry
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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