From local to global deformation quantization of Poisson manifolds

From local to global deformation quantization of Poisson manifolds

We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifold, based on M. Kontsevich's local formula. The deformed algebra of functions is realized as the algebra of horizontal sections of a vector bundle with flat connection.

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Veröffentlicht in:Duke mathematical journal 2002-11, Vol.115 (2), p.329-352
Hauptverfasser: Cattaneo, Alberto S., Felder, Giovanni, Tomassini, Lorenzo
Format: Artikel
Sprache:eng
Schlagworte:
53D17
53D55
Deformation quantization
Poisson groupoids and algebroids
Poisson manifolds
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Beschreibung
Zusammenfassung:We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifold, based on M. Kontsevich's local formula. The deformed algebra of functions is realized as the algebra of horizontal sections of a vector bundle with flat connection.
ISSN:0012-7094
1547-7398
DOI:10.1215/s0012-7094-02-11524-5