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Calculating an expression for trace of generators of two Lie algebra

  1. Jul 24, 2013 #1
    Suppose we have

    where Q's are generators of a Lie algebra associated a SU(N) group. So Q's are traceless. Also we have
    where P's are generators of a Lie algebra associated to an Abelian group. We have the following relation between these generators

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

    From the cyclic property of trace we have
    for any matrices. Also
    just for symmetric matrices. Maybe these relations help!

    Last edited: Jul 24, 2013
  2. jcsd
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