Lie Algebras of Hamiltonian Vector Fields and Symplectic Manifolds

摘要

We construct a local characteristic map to a symplectic manifold M via certain cohomology groups of Hamiltonian vector fields. For each p is an element of M, the Leibniz cohomology of the Hamiltonian vector fields on R-2n maps to the Leibniz cohomology of all Hamiltonian vector fields on M. For a particular extension g(n) of the symplectic Lie algebra, the Leibniz cohomology of g(n) is shown to be an exterior algebra on the canonical symplectic two-form. The Leibniz cohomology of this extension is then a direct summand of the Leibniz cohomology of all Hamiltonian vector fields on R-2n.