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Journal of Lie Theory 19 (2009), No. 2, 237--249
Copyright Heldermann Verlag 2009

Central Extensions of Coverings of Symplectomorphism Groups

Cornelia Vizman
West University of Timisoara, Dept. of Mathematics, Bd. V. Parvan 4, 300223 Timisoara, Romania

Each even dimensional submanifold of a symplectic manifold defines a Lie algebra 2-cocycle on the Lie algebra of symplectic vector fields. We study its integrability to the group of symplectic diffeomorphisms. When the submanifold is symplectic, we describe a coadjoint orbit of the corresponding extension.

Keywords: Coadjoint orbit, central extension.

MSC: 58B20

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