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Timeline for Twisted affine Lie algebras

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Feb 21, 2012 at 14:38 comment added Jim Humphreys @Angelo: That's true, which suggested to me that the discussion by Kac is perhaps a side issue, using analytic language to discuss Lie algebra automorphisms. Carter does construct and classify the affine and twisted affine algebras, using algebraic methods. What I'm not sure about is how explicitly the automorphisms of finite order have been treated algebraically in the literature (Kac and Helgason being the usual sources). The automorphism groups are themselves algebraic groups.
Feb 21, 2012 at 2:34 comment added Angelo @Jim: You motivated me to look at Carter's book once more. However, I am very surprised. Carter does not talk anything about the result that I am talking about!
Feb 18, 2012 at 23:42 history edited Jim Humphreys CC BY-SA 3.0
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Feb 18, 2012 at 21:19 comment added Angelo @Jim: Well, it is done in the page 126 of 3rd edition of Kac's book.
Feb 18, 2012 at 20:56 comment added Jim Humphreys @Angelo: I'd be surprised in this algebraic context if any serious use has to be made of complex exponentials, but that's not a proof.
Feb 18, 2012 at 20:21 comment added Angelo @Jim I agree with you and I tried many books, classics or not. When the approach is purely algebraically we can consider almost automatically for a general algebraically closed fields. However, the motivation for my question is because in the proof he uses the exponencial function of elements involving the complex number $i$. Of course we have $\sqrt{-1}$ in any algebraically closed field, but I need more faith that his demonstration works in general.
Feb 18, 2012 at 20:11 history answered Jim Humphreys CC BY-SA 3.0