Bicrossed products induced by Poisson vector fields and their integrability

Samson Apourewagne Djiba; Aïssa Wade

doi:10.1142/S0219887816500225

Bicrossed products induced by Poisson vector fields and their integrability

Samson Apourewagne Djiba
, Aïssa Wade

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

First we show that, associated to any Poisson vector field E on a Poisson manifold (M,p), there is a canonical Lie algebroid structure on the first jet bundle J1M which, depends only on the cohomology class of E. 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 L∞-Algebras.

Original language	English (US)
Article number	1650022
Journal	International Journal of Geometric Methods in Modern Physics
Volume	13
Issue number	3
DOIs	https://doi.org/10.1142/S0219887816500225
State	Published - Mar 1 2016

All Science Journal Classification (ASJC) codes

Physics and Astronomy (miscellaneous)

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10.1142/S0219887816500225

Cite this

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abstract = "First we show that, associated to any Poisson vector field E on a Poisson manifold (M,p), there is a canonical Lie algebroid structure on the first jet bundle J1M which, depends only on the cohomology class of E. 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 L∞-Algebras.",

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AB - First we show that, associated to any Poisson vector field E on a Poisson manifold (M,p), there is a canonical Lie algebroid structure on the first jet bundle J1M which, depends only on the cohomology class of E. 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 L∞-Algebras.

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Bicrossed products induced by Poisson vector fields and their integrability

Abstract

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