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Let $G$ be a connected reductive group over $\mathbb{C}$ of Lie algebra $\mathfrak{g}$.

What is the value of $H^{3}(\mathfrak{g}((t))((s)),\mathbb{C})$?

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  • $\begingroup$ A simply-connected group? Or just connected? $\endgroup$
    – David Roberts ♦
    Commented Sep 25, 2015 at 6:01
  • $\begingroup$ What does $\mathfrak{g}((t))((s))$ mean in this context? $\endgroup$
    – Christopher Drupieski
    Commented Sep 25, 2015 at 11:26
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    $\begingroup$ I put the most general assumption, but even the simply connected case would be interesting. In this context, $\mathfrak{g}((t))((s))=\mathfrak{g}\otimes_{k}k((t))((s))$. $\endgroup$
    – prochet
    Commented Sep 25, 2015 at 17:08

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