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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/10983

Title: Hochschild cohomology and Atiyah classes
Authors: Calaque, Damien
VAN DEN BERGH, Michel
Issue Date: 2010
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation: ADVANCES IN MATHEMATICS, 224(5). p. 1839-1889
Abstract: In this paper we prove that on a smooth algebraic variety the HKR-morphism twisted by the square root of the Todd genus gives an isomorphism between the sheaf of poly-vector fields and the sheaf of poly-differential operators, both considered as derived Gerstenhaber algebras. In particular we obtain an isomorphism between Hochschild cohomology and the cohomology of poly-vector fields which is compatible with the Lie bracket and the cupproduct. The latter compatibility is an unpublished result by Kontsevich. Our proof is set in the framework of Lie algebroids and so applies without modification in much more general settings as well. (C) 2010 Elsevier Inc. All rights reserved.
Notes: [Calaque, Damien] Univ Lyon 1, CNRS, UMR 5208, Inst Camille Jordan, F-69622 Villeurbanne, France. [Van den Bergh, Michel] Univ Hasselt, Dept WNI, B-3590 Diepenbeek, Belgium.
URI: http://hdl.handle.net/1942/10983
DOI: 10.1016/j.aim.2010.01.012
ISI #: 000278442800005
ISSN: 0001-8708
Category: A1
Type: Journal Contribution
Validation: ecoom, 2011
Appears in Collections: Research publications

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