Weyl manifolds and deformation quantization. (English) Zbl 0734.58011

Omori, Hideki; Maeda, Yoshiaki; Yoshioka, Akira

Adv. Math. 85, No. 2, 224-255 (1991).

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.

Reviewer: A.P.Stone (Albuquerque)

MSC:

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

Keywords:

deformation quantization; symplectic manifold; Weyl manifold

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