Integrability of central extensions of the Poisson Lie algebra via prequantization

B. Janssens, Cornelia Vizman

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Abstract

We present a geometric construction of central S 1-extensions of the quantomorphism group of a prequantizable, compact, symplectic manifold, and explicitly describe the corresponding lattice of integrable cocycles on the Poisson Lie algebra. We use this to find nontrivial central S 1-extensions of the universal cover of the group of Hamiltonian diffeomorphisms. In the process, we obtain central S1-extensions of Lie groups that act by exact strict contact transformations.

Original languageEnglish
Pages (from-to)1351-1375
Number of pages26
JournalJournal of Symplectic Geometry
Volume16
Issue number5
DOIs
Publication statusPublished - 2019

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