Hochschild cohomology of the Weyl algebra and traces in deformation quantization

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Duration: 3 min 30 s
Description: 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.
Boris Feigin; Giovanni Felder; Boris Shoikhet
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