Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Lie group (additional condition)

  1. Nov 25, 2004 #1
    Does somebody know an example of a differentiable manifold which is a group but NOT a Lie group? So the additional condition: the group operations multiplication and inversion are analytic maps, is not satisfied.
  2. jcsd
  3. Nov 25, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Yes, but they aren't particularly natural.

    Let M be any differential manifold. Let G be any group such that card(M)=card(G). Let f be any bijection of the underlying sets. Then F makes M into a group by fiat, and in general, if we pick f in completely arbitrary fashion, it will not be a lie group.

    More natural ones do not immediately spring to mind, sorry.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook