Foliated Lie and Courant Algebroids

  title={Foliated Lie and Courant Algebroids},
  author={Izu Vaisman},
  journal={Mediterranean Journal of Mathematics},
  • I. Vaisman
  • Published 8 February 2009
  • Mathematics
  • Mediterranean Journal of Mathematics
If A is a Lie algebroid over a foliated manifold $${(M, {\mathcal {F}})}$$, a foliation of A is a Lie subalgebroid B with anchor image $${T{\mathcal {F}}}$$ and such that A/B is locally equivalent with Lie algebroids over the slice manifolds of $${\mathcal F}$$. We give several examples and, for foliated Lie algebroids, we discuss the following subjects: the dual Poisson structure and Vaintrob's supervector field, cohomology and deformations of the foliation, integration to a Lie groupoid. In… 

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