most recent 30 from http://mathoverflow.net 2013-05-19T07:28:38Z http://mathoverflow.net/feeds/question/63636 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/63636/what-groups-are-lie-groups Mariano Suárez-Alvarez 2011-05-01T19:30:02Z 2011-05-01T19:51:55Z

<p>We know how to tell if a topological group is a Lie group: this was famously asked by Hilbert and answered gloriously by Gleason, Montgomery and Zippin in the 50s (a locally compact topological group can be turned into a Lie group iff there is one neighborhood of 1 which does not contain a non-trivial subgroup)</p> <blockquote> <p>Can one tell when an abstract group is in some way a Lie group?</p> </blockquote> <p>A natural follow up questions is, of course: if a group is Lie-sable (urgh), is it in a unique way? For comparison, a topological group which can made into a Lie group can be made in exactly one way.</p>