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Invariant cohomology of the Poisson Lie algebra of a symplectic manifold. (English) Zbl 0573.53024

The following theorem is shown: Let G be a subalgebra of the Lie algebra of Hamiltonian vectorfields on a symplectic manifold M. If M has a G- invariant connection, then the Chevalley cohomology generated by G- invariant differential cochains is isomorphic to the cohomology of the total complex.
Reviewer: C.G√ľnther

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
17B56 Cohomology of Lie (super)algebras
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