In Lemma 25, it seems that you are missing one forbidden subdiagram in order to be able to deduce Corollary 26 :

Three chains of simple edges of length {1, 3, 3} respectively, emenating from a common vertex.

It can also be checked by computing the determinant of the Gram matrix.

*[Corrected, thanks – T.]*

as for the signs in a Chevalley basis, I would like to mention that one can make a definite choice based on an idea of Lusztig, see my paper

Sincerely, Meinolf Geck

]]>*[Oops, you’re right, this conclusion of the corollary should be deleted (fortunately it isn’t the part of the corollary that is used elsewhere). -T.]*

Another typo: At the end of the proof of Lemma 23, should be .

*[Corrected, thanks – T.]*

“ to be trivial” or “ to be abelian”.

*[Corrected, thanks – T.]*

*[Corrected, thanks – T.]*

Sorry, I meant to say “derivation” rather than “automorphism” in my previous comments. (A derivation of Lie algebras is an infinitesimal version of an automorphism on Lie groups, in exactly the same way that a Lie bracket is an infinitesimal version of conjugation on a Lie group.)

]]>I am still not able to figure out why is an automorphism of for any . It seems it is obviously false when , and is not clear why it should be true for . Am I overlooking something?

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