Hochschild cohomology of the Weyl algebra and traces in deformation quantization

Details Hochschild cohomology of the Weyl algebra and traces in deformation quantization Hochschild cohomology of the Weyl algebra and traces in deformation quantization

2003-11-18

arxiv.org/abs/math/0311303v2

Duke Math. J. 127 (2005), no. 3, 487--517

Mathematics

Quantum Algebra

30 pages. Revised version

Scientific paper

10.1215/S0012-7094-04-12733-2

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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