### Abstract

For a connected symplectic manifold X, we determine the universal central extension of the Lie algebra ham(X) of hamiltonian vector fields. We classify the central extensions of ham(X), of the Lie algebra sp(X) of symplectic vector fields, of the Poisson Lie algebra C∞(X), and of its compactly supported version C∞c(X).

Original language | English |
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Pages (from-to) | 4996-5047 |

Number of pages | 52 |

Journal | International Mathematics Research Notices |

Volume | 2016 |

Issue number | 16 |

DOIs | |

Publication status | Published - 1 Oct 2015 |

Externally published | Yes |

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## Cite this

Janssens, B., & Vizman, C. (2015). Universal central extension of the Lie algebra of Hamiltonian vector fields.

*International Mathematics Research Notices*,*2016*(16), 4996-5047. https://doi.org/10.1093/imrn/rnv301