1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Manifolds / Lie Groups - confusing notation

  1. Mar 16, 2008 #1
    I'm reading over my Lie groups notes and in them, in the introductory section on manifolds, I've written that [itex]F_{\star}[/itex] is a commonly used notation for [itex]d_{x}F[/itex] and so the chain rule [itex]d_{x}{G \circ F}=d_{F(x)}G \circ d_{x}F[/itex] can be written [itex](G\circ F)_{\star}=G_{\star}\circ F_{\star}[/itex]

    Is what I've written correct? To me this seems horribly confusing since it neglects to mention where you are taking the differential. Should it instead be that [itex]F_{\star}[/itex] is the map from M to [itex]d_{x}F[/itex]. On second thoughts this doesn't make total sense either...

    He's gone on to make definitions like:

    A vector field X on a Lie group G is called left-invariant if, for all g,h in G, [itex](L_{g})_{\star}X_{h}=X_{gh}=X_{L_{g}(h)}[/itex] where [itex]L_{g}[/itex] is the left multiplication map by g ,which I'm finding difficult to understand with my current definition of [itex]F_{\star}[/itex].

    Thanks for any replies.
    Last edited: Mar 17, 2008
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?

Similar Discussions: Manifolds / Lie Groups - confusing notation
  1. Group theory (Replies: 0)