Hochschild cohomology of the Weyl algebra and traces in deformation quantization

Boris Feigin*, Giovanni Felder, Boris Shoikhet

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

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

Original languageEnglish
Pages (from-to)487-516
Number of pages30
JournalDuke Mathematical Journal
Volume127
Issue number3
DOIs
StatePublished - 15 Apr 2005
Externally publishedYes

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