On the splitting of infinitesimal Poisson automorphisms around symplectic leaves

A geometric description of the first Poisson cohomology groups is given in the semilocal context, around (possibly singular) symplectic leaves. This result is based on the splitting theorems for infinitesimal automorphisms of coupling Poisson structures which describe the interaction between the tan...

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Bibliographic Details
Published in:arXiv.org 2017-12
Main Authors: Velasco-Barreras, Eduardo, Vorobiev, Yury
Format: Article
Language:English
Subjects:
Automorphisms
Homology
Splitting
Online Access:Get full text
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Summary:A geometric description of the first Poisson cohomology groups is given in the semilocal context, around (possibly singular) symplectic leaves. This result is based on the splitting theorems for infinitesimal automorphisms of coupling Poisson structures which describe the interaction between the tangential and transversal data of the characteristic distributions. As a consequence, we derive some criteria of vanishing of the first Poisson cohomology groups and apply the general splitting formulas to some particular classes of Poisson structures associated with singular symplectic foliations.
ISSN:2331-8422