Lie algebraic characterization of manifolds |
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Authors: | Janusz Grabowski Norbert Poncin |
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Institution: | 1.Institute of Mathematics,Polish Academy of Sciences,Warsaw,Poland;2.Mathematics Laboratory,University of Luxembourg,Luxembourg City, Grand-Duchy of Luxembourg |
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Abstract: | Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential
operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold is characterized
by the corresponding Lie algebra of linear differential operators, i.e. isomorphisms of such Lie algebras are induced by the
appropriate class of diffeomorphisms of the underlying manifolds.
The research of Janusz Grabowski supported by the Polish Ministry of Scientific Research and Information Technology under
the grant No. 2 P03A 020 24, that of Norbert Poncin by grant C.U.L./02/010. |
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Keywords: | Algebraic characterization smooth real-analytic and Stein manifolds automorphism Lie algebras differential operators principal symbols |
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