= Antisymmetry of Killing-lowered structure constants
{title2=$c_{abc}=\kappa([t_a,t_b],t_c)$}
Lower the output index of the <structure constants of a Lie algebra> with its <Killing form>. The <Lie bracket> makes the result antisymmetric in the first two indices, while invariance gives $\kappa([t_a,t_b],t_c)=\kappa(t_a,[t_b,t_c])$, making it antisymmetric in the last two indices. These two adjacent transpositions imply total antisymmetry. Nondegeneracy of the <Killing form> is unnecessary.
// Target: lie-theory.bigb
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