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arXiv · 1508.00841

Integrability of central extensions of the Poisson Lie algebra via prequantization

Bas 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 S^1-extensions of Lie groups that act by exact strict contact transformations.

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Bas Janssens, Cornelia Vizman. 2015-08-04. Integrability of central extensions of the Poisson Lie algebra via prequantization. https://arxiv.org/abs/1508.00841

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