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seen May 24 '13 at 9:03
I am a graduate student in department of mathematics in Kansas State University. I am learning noncommutative algebraic geometry in the sense of Rosenberg and Kontsevich-Rosenberg

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comment Does Iwahori subalgebra correspond to any Cartan decomposition for affine Kac-Moody algebra?
Thank you very much! Yes, I realized that one can write down this decomposition which is very similar to "standard cartan decomposition" for affine Kac-Moody algebra(the only difference is replace $t^{-1}\mathbb{C}[t^{-1}]$ by $t\mathbb{C}[t]$ in standard one) and Cartan involution is like what you said: finite part and $t\mapsto t^{-1}$
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asked Does Iwahori subalgebra correspond to any Cartan decomposition for affine Kac-Moody algebra?