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For an algebraically closed field $\mathbb F$ of characteristic zero, a finite-dimensional Lie algebra $\frak G$ has a Cartan subalgebra and these subalgebras are conjugated in a certain sense.

Let $L(\frak G)= \frak G\otimes \mathbb F[t,t^{-1}]$ be the loop algebra associated to $\frak G$ with the natural bracket. Does exist a Cartan subalgebra for $L(\frak G)$? How to describe it?

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WHat is your definition of a Cartan algebra in this general situation? –  Mariano Suárez-Alvarez Jan 9 '12 at 21:19
Are you the same Matt as in math.stackexchange.com/users/22623/matt ? Are you having problems logging in? –  Mariano Suárez-Alvarez Jan 9 '12 at 21:20
Yes, I am. I have no idea why my login is not working. I am a new user, but I'm definitely going badly. –  Matt Jan 9 '12 at 21:31

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