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I think that "invariant element of " shoud be "invariant element of "? Basically , so I would expect invariant elements to do the same. Of course, the Killing form identifies and but it seems cleaner not to invoke the Killing form.
- You're correct; "*" is missing (as you can see from your proof as well as one in the article.) -- Taku (talk) 11:14, 7 April 2015 (UTC)
- Actually it was correct before; I think it's a matter of the notation. In the article (and elsewhere in Wikipedia), we write for the coordinate ring of (see ring of polynomial functions). That is, . Since "Sym" also appears in literature, that version is now also noted in the article. -- Taku (talk) 11:36, 7 April 2015 (UTC)