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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 | Source: | 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 The latter compatibility is an unpublished result by Kontsevich.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. | Keywords: | Deformation quantization; Atiyah classes | Document URI: | http://hdl.handle.net/1942/10983 | ISSN: | 0001-8708 | e-ISSN: | 1090-2082 | DOI: | 10.1016/j.aim.2010.01.012 | ISI #: | 000278442800005 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2011 |
Appears in Collections: | Research publications |
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0708.2725v4.pdf | 402.38 kB | Adobe PDF | View/Open |
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