We extend known prequantization procedures for Poisson and presym- plectic manifolds by defining the prequantization of a Dirac manifold P as a principal U(1)-bundle Q with a compatible Dirac-Jacobi structure. We study the action of Poisson algebras of admissible functions on P on various spaces of locally (with respect to P) defined functions on Q, via hamiltonian vector fields. Finally, guided by examples arising in complex analysis and contact geometry, we propose an extension of the notion of prequantization in which the action of U(1) on Q is permitted to have some fixed points. Dedicated to the memory of Professor Shiing-Shen Chern.

Weinstein, A; Zambon, M (2005). *Variations on prequantization.* In: Molitor-Braun, C; Poncin, N; Schlichenmaier, M. Travaux mathématiques XVI. Luxembourg: Faculty of Science, Technology and Communication. University of Luxembourg, 187-219.

## Abstract

We extend known prequantization procedures for Poisson and presym- plectic manifolds by defining the prequantization of a Dirac manifold P as a principal U(1)-bundle Q with a compatible Dirac-Jacobi structure. We study the action of Poisson algebras of admissible functions on P on various spaces of locally (with respect to P) defined functions on Q, via hamiltonian vector fields. Finally, guided by examples arising in complex analysis and contact geometry, we propose an extension of the notion of prequantization in which the action of U(1) on Q is permitted to have some fixed points. Dedicated to the memory of Professor Shiing-Shen Chern.

## Citations

## Altmetrics

## Additional indexing

Other titles: | Proceedings of the 4th Conference on Poisson Geometry held at the University of Luxembourg, Luxembourg City, June 7–11, 2004 |
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Item Type: | Book Section, refereed, original work |

Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Language: | English |

Date: | 2005 |

Deposited On: | 29 Nov 2010 16:26 |

Last Modified: | 05 Apr 2016 13:24 |

Publisher: | Faculty of Science, Technology and Communication. University of Luxembourg |

Series Name: | Travaux mathématiques |

Number: | 17 |

ISBN: | 2-87971-253-X |

Free access at: | Official URL. An embargo period may apply. |

Official URL: | http://math.uni.lu/travaux/Last/10WEIN.PDF |

Related URLs: | http://www.ams.org/mathscinet-getitem?mr=2223158 http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1119.53060 |

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