Geodesic
Central Extensions of the Lie Algebra of Symplectic Vector Fields
Journal of Lie theory, Tome 16 (2006) no. 2, pp. 297-309

Voir la notice de l'article provenant de la source Heldermann Verlag

\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.
Classification : 17B56, 17B66
Mots-clés : Central extension, symplectic and Hamiltonian vector field 
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     author = {C. Vizman },
     title = {Central {Extensions} of the {Lie} {Algebra} of {Symplectic} {Vector} {Fields}},
     journal = {Journal of Lie theory},
     pages = {297--309},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2006},
     url = {http://geodesic.mathdoc.fr/item/JLT_2006_16_2_JLT_2006_16_2_a5/}
}
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C. Vizman . Central Extensions of the Lie Algebra of Symplectic Vector Fields. Journal of Lie theory, Tome 16 (2006) no. 2, pp. 297-309. http://geodesic.mathdoc.fr/item/JLT_2006_16_2_JLT_2006_16_2_a5/