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.


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