Reference : Deformations of pre-symplectic structures and the Koszul L-infty-algebra |

E-prints/Working papers : Already available on another site | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/31775 | |||

Deformations of pre-symplectic structures and the Koszul L-infty-algebra | |

English | |

Schätz, Florian [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Zambon, Marco [Katholieke Universiteit Leuven - KUL > Mathematics] | |

2017 | |

2 | |

44 | |

No | |

[en] pre-symplectic structures ; Dirac geometry ; deformation theory | |

[en] We study the deformation theory of pre-symplectic structures, i.e. closed two-forms of fixed rank. The main result is a parametrization of nearby deformations of a given pre-symplectic structure in terms of an $L_\infty$-algebra, which we call the Koszul $L_\infty$-algebra. This
$L_\infty$-algebra is a cousin of the Koszul dg Lie algebra associated to a Poisson manifold, and its proper geometric understanding relies on Dirac geometry. In addition, we show that a quotient of the Koszul $L_{\infty}$-algebra is isomorphic to the $L_\infty$-algebra which controls the deformations of the underlying characteristic foliation. Finally, we show that the infinitesimal deformations of pre-symplectic structures and of foliations are both obstructed. | |

http://hdl.handle.net/10993/31775 | |

https://arxiv.org/abs/1703.00290 |

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