Local Lie algebra determines base manifold

Details Local Lie algebra determines base manifold Local Lie algebra determines base manifold

2005-06-28

arxiv.org/abs/math/0506565v2

In "From Geometry to Quantum Mechanics, in Honor of Hideki Omori", Y.Maeda et al., eds., Progress in Math. 252, Birkhaeuser (2

Mathematics

Differential Geometry

13 pages, minor corrections, to appear in "From Geometry to Quantum Mechanics, in Honor of Hideki Omori", Y.Maeda et al., eds.

Scientific paper

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.

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