Hochschild cohomology of the Weyl algebra and traces in deformation quantization
arXiv:math/0311303 · doi:10.1215/S0012-7094-04-12733-2
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.
30 pages. Revised version