On deformations of Lie algebroids

Details On deformations of Lie algebroids On deformations of Lie algebroids

2010-04-17

arxiv.org/abs/1004.2959v2

Mathematics

Differential Geometry

17 pages, to appear in Results in Mathematics

Scientific paper

For any Lie algebroid A, its 1-jet bundle JA is a Lie algebroid naturally and there is a representation \pi: JA ->DA. Denote by dJ 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(Hom(^\bulletJA,A)DA), dJ) of the cochain complex (\Gamma(Hom(^\bulletJA,A)), dJ).

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