Duke Mathematical Journal

From local to global deformation quantization of Poisson manifolds

Alberto S. Cattaneo, Giovanni Felder, and Lorenzo Tomassini

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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.

Article information

Duke Math. J., Volume 115, Number 2 (2002), 329-352.

First available in Project Euclid: 26 May 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D55: Deformation quantization, star products
Secondary: 53D17: Poisson manifolds; Poisson groupoids and algebroids


Cattaneo, Alberto S.; Felder, Giovanni; Tomassini, Lorenzo. From local to global deformation quantization of Poisson manifolds. Duke Math. J. 115 (2002), no. 2, 329--352. doi:10.1215/S0012-7094-02-11524-5. https://projecteuclid.org/euclid.dmj/1085598145

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