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Hochschild cohomology of the Weyl algebra and traces in deformation quantization

Boris Feigin·Giovanni Felder·Boris Shoikhet
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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 non-commutative version of formal geometry, we obtain an explicit expression for the canonical trace in deformation quantization of symplectic manifolds.

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Boris Feigin, Giovanni Felder, Boris Shoikhet. 2005-04-26. Hochschild cohomology of the Weyl algebra and traces in deformation quantization. https://doi.org/10.1215/s0012-7094-04-12733-2

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