Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 16 (2006), No. 2, 297--309Copyright Heldermann Verlag 2006 Central Extensions of the Lie Algebra of Symplectic Vector Fields Cornelia Vizman West University of Timisoara, Dept. of Mathematics, Bd. V. Parvan 4, 300223 Timisoara, Romania vizman@math.uvt.ro [Abstract-pdf] \def\g{{\frak g}} \def\h{{\frak h}} For a perfect ideal $\h$ of the Lie algebra $\g$, the extendibility of continuous 2-cocycles from $\h$ to $\g$ is studied, especially for 2-cocycles of the form $\langle[X,\cdot],\cdot\rangle$ on $\h$ with $X\in\g$, when a $\g$-invariant symmetric bilinear form $\langle\cdot, \cdot\rangle$ on $\h$ is available. The results are then applied to extend continuous 2-cocycles from the Lie algebra of Hamiltonian vector fields to the Lie algebra of symplectic vector fields on a compact symplectic manifold. Keywords: Central extension, symplectic and Hamiltonian vector field. MSC: 17B56, 17B66 [ Fulltext-pdf  (200  KB)] for subscribers only.