From: "Malcolm Black" Subject: Re: Lie algebras of vector fields Date: Sat, 20 Jan 2001 21:46:46 +0100 Newsgroups: sci.math.research Summary: Characterizing manifolds by their Lie algebras of vector fields Dear Paul, well, I'm not an expert in these matters, but I've just been reading: Hideki Omori, Infinite Dimensional Lie Transformation Groups, Springer Lecture Notes in Math. 427, 1974. Omori (Chap. X) attributes the result you're looking for to Pursell and Shanks (Proc. Amer. Math. Soc. 1954, 468-472) and goes further to extend the result to certain sub-algebras, preserving volume forms, contact forms,... Compactness does not appear to be necessary. Malcolm Black EMail: MalcolmBlack@web.de Paul R. Chernoff schrieb in Nachricht <94bu7u$e8$1@agate.berkeley.edu>... >Let M be a smooth finite-dimensional manifold (perhaps compact), >and let Vect(M) denote the Lie algebra of (perhaps compactly supported) >smooth vector fields on M. If Vect(M) and Vect(N) are isomorphic as Lie >algebras, is M diffeomorphic to N? (And is the isomorphism of the >Lie algebras induced by the diffeomorphism in the obvious way?) > > >-- ># Paul R. Chernoff chernoff@math.berkeley.edu # ># Department of Mathematics 3840 # ># University of California "Against stupidity, the gods themselves # ># Berkeley, CA 94720-3840 struggle in vain." -- Schiller #