Here's an excerpt from this lecture script:
And another one:
Why is there a relationship between the Killing form and the quadratic Casimir invariant?
Asked
Active
Viewed 346 times
1
-
Note that the $\mathfrak{g}_\alpha$ refers to the Cartan grading and assumes $\mathfrak{g}$ semisimple in the notes you quote. – YCor Mar 23 '17 at 18:13
-
@YCor I see. Well, it's a bit of a "maths for physicists" script, so it might well be that there are assumptions that are not written out. But do you understand why Killing forms and quadratic Casimir invariants are inversions of each other? – Andy Miles Mar 24 '17 at 14:18