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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.
  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!
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