Hochschild cohomology for Lie algebroids
arXiv:0908.2630 · doi:10.1093/imrn/rnq033
Abstract
We define the Hochschild (co)homology of a ringed space relative to a locally free Lie algebroid. Our definitions mimic those of Swan and Caldararu for an algebraic variety. We show that our (co)homology groups can be computed using suitable standard complexes. Our formulae depend on certain natural structures on jetbundles over Lie algebroids. In an appendix we explain this by showing that such jetbundles are formal groupoids which serve as the formal exponentiation of the Lie algebroid.
The authors were informed that the fact that jetbundles are formal groupoids is already contained in arXiv:0904.4736 (with a somewhat different proof)