TY - JOUR
T1 - On the splitting of infinitesimal Poisson automorphisms around symplectic leaves
AU - Velasco-Barreras, Eduardo
AU - Vorobiev, Yury
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2018/8
Y1 - 2018/8
N2 - 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.
AB - 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.
KW - Coupling Poisson structure
KW - Infinitesimal automorphism
KW - Poisson cohomology
KW - Singular foliation
KW - Symplectic leaf
UR - http://www.scopus.com/inward/record.url?scp=85044443888&partnerID=8YFLogxK
U2 - 10.1016/j.difgeo.2018.03.002
DO - 10.1016/j.difgeo.2018.03.002
M3 - Artículo
SN - 0926-2245
VL - 59
SP - 12
EP - 34
JO - Differential Geometry and its Application
JF - Differential Geometry and its Application
ER -