Lie algebraic characterization of manifolds

Details Lie algebraic characterization of manifolds Lie algebraic characterization of manifolds

2003-10-14

arxiv.org/abs/math/0310202v2

Central European Journal of Mathematics, 2(5) 2004, pp. 811-825

Mathematics

Differential Geometry

15 pages

Scientific paper

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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