Duke Mathematical Journal

Hochschild cohomology of the Weyl algebra and traces in deformation quantization

Boris Feigin, Giovanni Felder, and Boris Shoikhet

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We give a formula for a cocycle generating the Hochschild cohomology of the Weyl algebra with coefficients in its dual. It is given by an integral over the configuration space of ordered points on a circle. Using this formula and a noncommutative version of formal geometry, we obtain an explicit expression for the canonical trace in deformation quantization of symplectic manifolds.

Article information

Duke Math. J., Volume 127, Number 3 (2005), 487-517.

First available in Project Euclid: 18 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
Secondary: 53D55: Deformation quantization, star products


Feigin, Boris; Felder, Giovanni; Shoikhet, Boris. Hochschild cohomology of the Weyl algebra and traces in deformation quantization. Duke Math. J. 127 (2005), no. 3, 487--517. doi:10.1215/S0012-7094-04-12733-2. https://projecteuclid.org/euclid.dmj/1113847337

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