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Question about SO(N) group generators

  1. Jan 20, 2013 #1
    Hi all. I have a question about the properties of the generators of the SO(N) group.
    What kind of commutation relation they satisfy? Is it true that the generators λ are such that:

    $$\lambda^T=-\lambda$$ ??

    Thank you very much
  2. jcsd
  3. Jan 21, 2013 #2
    The commutators are complicated, in general--or too complicated for me.

    Yes, the Lie algebra of SO(n) is the skew-symmetric matrices, which is the condition you wrote. That comes from differentiating a path of orthogonal matrices at the identity, or rather differentiating the equation that defines an orthogonal matrix.
  4. Jan 21, 2013 #3
    Notice, that the n-dimensionality of SO(n) are triangle numbers in ℝn hopefully this can help you figure out a reason why, also I set a link to a video I think that might be able to help.


    Edit: Also may I ask why do you need to know this thing about the lie commutators in SO(n)?
    Last edited by a moderator: Sep 25, 2014
  5. Jan 22, 2013 #4
    Thank you very much! That solves some problems!

    I am working on the SO(N) symmetry of a [itex]\lambda \phi^4[/itex] theory in QFT and I need the exact expression of the commutator of two conserved charges, so I need to know the commutator of the generators.
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