
Journal of Lie Theory 16 (2006), No. 2, 297309 Copyright 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 [Abstractpdf] \def\g{{\frak g}} \def\h{{\frak h}} For a perfect ideal $\h$ of the Lie algebra $\g$, the extendibility of continuous 2cocycles from $\h$ to $\g$ is studied, especially for 2cocycles 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 2cocycles 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 [ Fulltextpdf (200 KB)] for subscribers only. 