Lie algebraic characterization of manifolds

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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 underlaying manifolds.
15 pages

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Differential Geometry, 17B63; 13N10; 16S32; 17B40; 17B65; 53D17

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http://salesiana.dossiersoluciones.com/handle/123456789/68846

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0310202
 http://arxiv.org/abs/math/0310202
 Central European Journal of Mathematics, 2(5) 2004, pp. 811-825

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arXiv