Local Lie algebra determines base manifold

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dc.creatorGrabowski, Janusz
dc.date2005-06-28
dc.date2006-08-26
dc.date.accessioned2026-07-07T07:47:19Z
dc.date.available2026-07-07T07:47:19Z
dc.descriptionIt is proven that a local Lie algebra in the sense of A. A. Kirillov determines the base manifold up to a diffeomorphism provided the anchor map is nowhere-vanishing. In particular, the Lie algebras of nowhere-vanishing Poisson or Jacobi brackets determine manifolds. This result has been proven for different types of differentiability: smooth, real-analytic, and holomorphic.
dc.description13 pages, minor corrections, to appear in "From Geometry to Quantum Mechanics, in Honor of Hideki Omori", Y.Maeda et al., eds., Progress in Math. 252, Birkhaeuser 2007
dc.identifierhttps://arxiv.org/abs/math/0506565
dc.identifierhttp://arxiv.org/abs/math/0506565
dc.identifierIn "From Geometry to Quantum Mechanics, in Honor of Hideki Omori", Y.Maeda et al., eds., Progress in Math. 252, Birkhaeuser (2007),131-145
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124124
dc.subjectDifferential Geometry
dc.subjectRings and Algebras
dc.subject17B66; 53D10; 53D17
dc.titleLocal Lie algebra determines base manifold
dc.typetext

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