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

Is there such an identity about SO(3)?

  1. May 28, 2006 #1
    [tex]T^i K_{ij} = K T^j K^{-1}[/tex]
    repeated indices imply summation.
    [tex]T^i[/tex] are the generators (Lie algebra elements) of SO(3).
    i.e.[tex]T^i_{jk} = - \epsilon_{ijk}[/tex]
    [tex]T^i \in so(3)[/tex]
    [tex]K \in SO(3)[/tex]

    How to show it's true?
    Is there a universal formula for all Lie group?
    Last edited: May 28, 2006
  2. jcsd
  3. May 28, 2006 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Those elements do not generate SO(3). SO(3) is uncountable, it cannot have a finte set of generators.
  4. May 28, 2006 #3

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    For physicists, generators of a Lie group are elements of the corresponding Lie algebra, or maybe such elements multiplied by i. I don't know what the K's are.
  5. May 28, 2006 #4
    Yes. I have just clarified!
    I also checked a special case, and it's true.
    I don't know how to prove this identity besides brute-force calculation which gives no insight at all.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Is there such an identity about SO(3)?
  1. Elements of SO(3)? (Replies: 13)