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Journal of Lie Theory 16 (2006), No. 2, 297--309
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


\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

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