Hochschild cohomology of the Weyl algebra and traces in deformation quantization

By Boris Feigin, Giovanni Felder, B. Shoikhet. 2003

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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 non-commutative version of formal geometry, we obtain an explicit expression for the canonical trace in deformation quantization of symplectic manifolds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ccf4811b42c57cad3510c8d6b54a0ee864a36039