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

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.

    Link:


    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Question about SO(N) group generators
Loading...