TY - JOUR
T1 - Bicrossed products induced by Poisson vector fields and their integrability
AU - Djiba, Samson Apourewagne
AU - Wade, Aïssa
N1 - Publisher Copyright:
© 2016 World Scientific Publishing Company.
PY - 2016/3/1
Y1 - 2016/3/1
N2 - 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.
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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U2 - 10.1142/S0219887816500225
DO - 10.1142/S0219887816500225
M3 - Article
AN - SCOPUS:84959873235
SN - 0219-8878
VL - 13
JO - International Journal of Geometric Methods in Modern Physics
JF - International Journal of Geometric Methods in Modern Physics
IS - 3
M1 - 1650022
ER -