Journal of Lie Theory

no. 2
Central Extensions of the Lie Algebra of Symplectic Vector Fields
Journal of Lie Theory, Volume 16 (2006) no. 2, pp. 297-309
\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.
DOI: 10.5802/jolt.411
Classification: 17B56, 17B66
Keywords: Central extension, symplectic and Hamiltonian vector field 
@article{JOLT_2006_16_2_a5,
     author = {C. Vizman},
     title = {Central {Extensions} of the {Lie} {Algebra} of {Symplectic} {Vector} {Fields}},
     journal = {Journal of Lie Theory},
     pages = {297--309},
     year = {2006},
     volume = {16},
     number = {2},
     doi = {10.5802/jolt.411},
     zbl = {1128.17017},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.411/}
}
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C. Vizman. Central Extensions of the Lie Algebra of Symplectic Vector Fields. Journal of Lie Theory, Volume 16 (2006) no. 2, pp. 297-309. doi: 10.5802/jolt.411

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