2003/10/31 by Janusz Grabowski, Norbert Poncin
Mathematics · #math.DG #msc:17B63 #msc:13N10 #msc:16S32 #msc:17B40 #msc:17B65 #msc:53D17
published as Central European Journal of Mathematics, 2(5) 2004, pp. 811-825 · 15 pages
arxiv created 2005/02/03 · arxiv updated 2009/12/01
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.