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

Calculating an expression for trace of generators of two Lie algebra

  1. Jul 24, 2013 #1
    Suppose we have
    $$[Q^a,Q^b]=if^c_{ab}Q^c$$

    where Q's are generators of a Lie algebra associated a SU(N) group. So Q's are traceless. Also we have
    $$[P^a,P^b]=0$$
    where P's are generators of a Lie algebra associated to an Abelian group. We have the following relation between these generators
    $$[Q^a,P^b]=if^c_{ab}P^c$$

    I would like to know what we can say above the following trace. Is it equal to zero?
    $$tr([Q^a,P^b]Q^c P^d)$$

    Comment:
    From the cyclic property of trace we have
    $$tr[A,B]=0$$
    for any matrices. Also
    $$tr([A,B]C)=0$$
    just for symmetric matrices. Maybe these relations help!



    Cheers!
     
    Last edited: Jul 24, 2013
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Calculating an expression for trace of generators of two Lie algebra
  1. Lie algebra concept (Replies: 1)

Loading...