Hochschild cohomology for Lie algebroids

Details Hochschild cohomology for Lie algebroids Hochschild cohomology for Lie algebroids

2009-08-18

arxiv.org/abs/0908.2630v3

International Mathematical Research Notices 2010 (2010), no. 21, 4098--4136

Mathematics

Algebraic Geometry

The authors were informed that the fact that jetbundles are formal groupoids is already contained in arXiv:0904.4736 (with a s

Scientific paper

10.1093/imrn/rnq033

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.

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