How Is the Killing Metric Normalized for Compact Simple Groups?

[center o bass]

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?

 

[Greg Bernhardt]

I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?

 

[Pond Dragon]

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?

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?