Duke Mathematical Journal

From local to global deformation quantization of Poisson manifolds

Alberto S. Cattaneo, Giovanni Felder, and Lorenzo Tomassini

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Abstract

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

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

Dates
First available in Project Euclid: 26 May 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1085598145

Digital Object Identifier
doi:10.1215/S0012-7094-02-11524-5

Mathematical Reviews number (MathSciNet)
MR1944574

Zentralblatt MATH identifier
1037.53063

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

Citation

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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References

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