Foliated Lie and Courant Algebroids

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If A is a Lie algebroid over a foliated manifold (M, F), a foliation of A is a Lie subalgebroid B with anchor image TF and such that A/B is locally equivalent with Lie algebroids over the slice manifolds of 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 the last section, we define a corresponding notion of a foliation of a Courant algebroid A as a bracket-closed, isotropic subbundle B with anchor image TF and such that B/B is locally equivalent with Courant algebroids over the slice manifolds of F. Examples that motivate the definition are given.

Original languageEnglish
Pages (from-to)415-444
Number of pages30
JournalMediterranean Journal of Mathematics
Issue number4
StatePublished - Dec 2010


  • Courant algebroid
  • Foliation
  • Lie algebroid

ASJC Scopus subject areas

  • General Mathematics


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