Hochschild cohomology of the Weyl algebra and traces in deformation quantization

Boris Feigin; Giovanni Felder; Boris Shoikhet

doi:10.1215/S0012-7094-04-12733-2

Hochschild cohomology of the Weyl algebra and traces in deformation quantization

Boris Feigin^*, Giovanni Felder, Boris Shoikhet

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	487-516
Number of pages	30
Journal	Duke Mathematical Journal
Volume	127
Issue number	3
DOIs	https://doi.org/10.1215/S0012-7094-04-12733-2
State	Published - 15 Apr 2005
Externally published	Yes

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AB - 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.

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Hochschild cohomology of the Weyl algebra and traces in deformation quantization

Abstract

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