Well, based on the generality you pointed out at inner product, I can accept it being whatever signature. But I think a note should be added pointing out it only gives a norm hence a metric when positive definite, perhaps according to the red herring principle.

]]>I am wondering if you would be satisfied with the evident answer: “No.” Or “No, and there is the usual sign convention.”

]]>Is the bilinear form assumed to be positive definite? If so, then we need the *negative* of the Killing form on a semisimple Lie algebra, as the bare Killing form is *negative* definite on such a Lie algebra (and in fact this characterises semisimple Lie algebras!)

added a table (here) showing the string-diagrammtics of the structure of a metric Lie algebra

]]>starting some minimum

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