Central Extensions of the Lie Algebra of Symplectic Vector Fields

C. Vizman

Journal of Lie Theory, Tome 16 (2006) no. 2, pp. 297-309

Résumé

\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.

Détail

Classification : 17B56, 17B66
Mots-clés : Central extension, symplectic and Hamiltonian vector field