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Killing metric on compact simple groups

  1. Jul 29, 2014 #1
    The killing form can be defined as the two-form ##K(X,Y) = \text{Tr} ad(X) \circ ad(Y)## and it has matrix components ##K_{ab} = c^{c}_{\ \ ad} c^{d}_{\ \ bc}##. I have often seen it stated that for a compact simple group we can normalize this metric by
    ##K_{ab} = k \delta_{ab}## for some proportionality constant ##k##. How is this statement proved?
     
    Last edited: Jul 29, 2014
  2. jcsd
  3. Aug 14, 2014 #2
    I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?
     
  4. Aug 15, 2014 #3
    Can you give a source for where you "often" see it? I'm having trouble understanding what you want. Are you asking if the Killing form is a metric?
     
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