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
help_outline
https://doi.org/10.4310/JSG.2018.v16.n5.a4
More Info
expand_more

Published Date

2019

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

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.

Files

1508.00841.pdf
(.pdf | 0.352 Mb)