Integrability of central extensions of the Poisson Lie algebra via prequantization

Journal article (2019)

Authors

B. Janssens Analysis - EEMCS
Cornelia Vizman West University of Timisoara (UVT)
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2019 B. Janssens, Cornelia Vizman
DOI: https://doi.org/10.4310/JSG.2018.v16.n5.a4
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Published Date

2019

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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.

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