## Abstract

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 language | English |
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Pages (from-to) | 415-444 |

Number of pages | 30 |

Journal | Mediterranean Journal of Mathematics |

Volume | 7 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2010 |

## Keywords

- Courant algebroid
- Foliation
- Lie algebroid

## ASJC Scopus subject areas

- Mathematics (all)