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(adsbygoogle = window.adsbygoogle || []).push({});

##K_{ab} = k \delta_{ab}## for some proportionality constant ##k##. How is this statement proved?

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# Killing metric on compact simple groups

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