Corpus ID: 174801234

Central extensions of Lie groups preserving a differential form.

@article{Diez2019CentralEO,
  title={Central extensions of Lie groups preserving a differential form.},
  author={T. Diez and B. Janssens and Karl-Hermann Neeb and Cornelia Vizman},
  journal={arXiv: Differential Geometry},
  year={2019}
}
  • T. Diez, B. Janssens, +1 author Cornelia Vizman
  • Published 2019
  • Mathematics
  • arXiv: Differential Geometry
  • Let $M$ be a manifold with a closed, integral $(k+1)$-form $\omega$, and let $G$ be a Fr\'echet-Lie group acting on $(M,\omega)$. As a generalization of the Kostant-Souriau extension for symplectic manifolds, we consider a canonical class of central extensions of $\mathfrak{g}$ by $\mathbb{R}$, indexed by $H^{k-1}(M,\mathbb{R})^*$. We show that the image of $H_{k-1}(M,\mathbb{Z})$ in $H^{k-1}(M,\mathbb{R})^*$ corresponds to a lattice of Lie algebra extensions that integrate to smooth central… CONTINUE READING

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