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

Lie subalgebra and subspace

  1. Mar 12, 2008 #1
    I have a question about Lie subalgebra.

    They say "a Lie subalgebra is a much more CONSTRAINED structure than a subspace".
    Well, it seems subtle, and I find this very tricky to follow.

    Can anyone explain this with concrete examples?

    If my question is not clear, please tell me so, I will try to rephrase it.
    Thanks.
     
  2. jcsd
  3. Mar 12, 2008 #2
    an algebra is nececearily not a space (understood vectorspace), so there is a big different. If you are talking about an subalgebra and a lie subalgebra. I guess you know the usual deffinition of a subalgebra, a lie subalgebra is a much more strict because a lie subalgebra needs to be a algebra + a submanifold, which is very strict.
     
  4. Mar 12, 2008 #3
    KarateMan: A Lie subalgebra is a linear subspace which is a Lie algebra.
    Hence, besides being a subspace, it has to satisfy the Lie algebra axioms (e.g. it has to be closed under the Lie bracket!).

    mrandersdk: There are no topological requirements for Lie (sub)algebras.
     
  5. Mar 12, 2008 #4
    This is terribly, terribly wrong.
     
  6. Mar 13, 2008 #5
    so sorry always do this, i read it as lie group, why do i always do this. Sorry again.

    Neglect my comment.
     
  7. Mar 16, 2008 #6
    Thanks everyone. took me a while but I think I swallowed it!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Lie subalgebra and subspace
  1. The lie brocket (Replies: 8)

  2. Lie Groups (Replies: 7)

  3. Lie algebra (Replies: 1)

Loading...