Local Lie algebra determines base manifold

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It 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.
13 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

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Differential Geometry, Rings and Algebras, 17B66; 53D10; 53D17

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http://salesiana.dossiersoluciones.com/handle/123456789/124124

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0506565
 http://arxiv.org/abs/math/0506565
 In "From Geometry to Quantum Mechanics, in Honor of Hideki Omori", Y.Maeda et al., eds., Progress in Math. 252, Birkhaeuser (2007),131-145

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arXiv