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Bicrossed products induced by Poisson vector fields and their integrability
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First we show that, associated to any Poisson vector field [Formula: see text] on a Poisson manifold [Formula: see text], there is a canonical Lie algebroid structure on the first jet bundle [Formula: see text] which, depends only on the cohomology class of [Formula: see text]. We then introduce the notion of a cosymplectic groupoid and we discuss the integrability of the first jet bundle into a cosymplectic groupoid. Finally, we give applications to Atiyah classes and [Formula: see text]-algebras.
World Scientific Pub Co Pte Ltd
Title: Bicrossed products induced by Poisson vector fields and their integrability
Description:
First we show that, associated to any Poisson vector field [Formula: see text] on a Poisson manifold [Formula: see text], there is a canonical Lie algebroid structure on the first jet bundle [Formula: see text] which, depends only on the cohomology class of [Formula: see text].
We then introduce the notion of a cosymplectic groupoid and we discuss the integrability of the first jet bundle into a cosymplectic groupoid.
Finally, we give applications to Atiyah classes and [Formula: see text]-algebras.
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