# Foliated Lie and Courant Algebroids

@article{Vaisman2009FoliatedLA,
title={Foliated Lie and Courant Algebroids},
author={Izu Vaisman},
journal={Mediterranean Journal of Mathematics},
year={2009},
volume={7},
pages={415-444}
}
• 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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