Talk:Nilpotent Lie algebra

Can some way clarify what is ${\mathfrak {gl}}_{k}$ ? —Preceding unsigned comment added by Malaggan (talk • contribs) 17:07, 29 July 2010 (UTC)[reply]

I think that it's assumed if you're on the Nilpotent Lie Algebra page, you have some experience with Lie algebras - and

{\mathfrak {gl}}_{k}

is the first one you come across. I'll put something in, though. Myrkkyhammas (talk) 16:49, 17 February 2011 (UTC)[reply]

What is an outer automorphism of a Lie algebra?

I have a problem with the statement that the Lie algebra admits an outer automorphism. What is meant by that? I know what an outer automorphism of a group is and I know what an outer derivation of a Lie algebra is. Can someone clarify that? Thank you. --130.83.2.27 (talk) 12:49, 3 July 2014 (UTC)[reply]

It must mean an automorphism that is not in the image of Ad. 84.226.185.221 (talk) 02:51, 11 October 2015 (UTC)[reply]

Rewrote Definition section as "Equivalent conditions"

The best I could tell, the previous Definitions section was logically incoherent. I could not get a proof of Engel's theorem out of it, and I couldn't tell if one was being claimed. The remaining claims were not very well announced or summarized, and yet some of them seemed to repeat themselves. Perhaps there was more there than I saw, but if so, it needs to be pointed out clearly. 84.226.185.221 (talk) 02:59, 11 October 2015 (UTC)[reply]

The reasoning in the previous definition section was taken from Knapp's book, including the statement about Engel's theorem (if I recall correctly). Engel's theorem was not proved, merely stated; the fact that ad-nilpotency of every element

g

implies nilpotency of

g

is the real content of Engel's theorem. (The other direction is near trivial.) But I agree that my formulation of things was a bit cryptic. (Perhaps not my finest moment.) The current version is much clearer and more to the point. YohanN7 (talk) 09:54, 13 October 2015 (UTC)[reply]