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Lie algebraic characterization of manifolds

Janusz Grabowski·Norbert Poncin
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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 underlaying manifolds.

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Janusz Grabowski, Norbert Poncin. 2005-02-03. Lie algebraic characterization of manifolds. https://arxiv.org/abs/math/0310202

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