Abstract
For any Lie algebroid A, its 1-jet bundle \({\mathfrak{J} A}\) is a Lie algebroid naturally and there is a representation \({\pi:\mathfrak{J} A\longrightarrow\mathfrak{D} A}\) . Denote by \({{\rm d}_{\mathfrak{J}}}\) the corresponding coboundary operator. In this paper, we realize the deformation cohomology of a Lie algebroid A introduced by M. Crainic and I. Moerdijk as the cohomology of a subcomplex \({(\Gamma({\rm Hom}(\wedge^\bullet\mathfrak{J} A,A)_{{\mathfrak{D}} A}),{\rm d}_{\mathfrak{J}})}\) of the cochain complex \({(\Gamma({\rm Hom}(\wedge^\bullet\mathfrak{J} A, A)),{\rm d}_\mathfrak{J})}\) .
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Research partially supported by NSFC (10871007,11026046), SRFDP (20100061120096), China Postdoctoral Science Foundation (20090451267) and the Fundamental Research Funds for the Central Universities (200903294).
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Sheng, Y. On Deformations of Lie Algebroids. Results. Math. 62, 103–120 (2012). https://doi.org/10.1007/s00025-011-0133-x
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DOI: https://doi.org/10.1007/s00025-011-0133-x