Universal central extension of the Lie algebra of Hamiltonian vector fields. (English) Zbl 1404.17035
Summary: For a connected symplectic manifold \(X\), we determine the universal central extension of the Lie algebra \(\mathrm{ham}(X)\) of hamiltonian vector fields. We classify the central extensions of \(\mathrm{ham}(X)\), of the Lie algebra \(\mathrm{sp}(X)\) of symplectic vector fields, of the Poisson Lie algebra \(C^\infty (X)\), and of its compactly supported version \(C^\infty_c (X)\).
MSC:
17B65 | Infinite-dimensional Lie (super)algebras |
17B56 | Cohomology of Lie (super)algebras |
17B63 | Poisson algebras |
53D17 | Poisson manifolds; Poisson groupoids and algebroids |