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Non-invariant forms on loop Lie algebra of semisimple Lie group

Let us consider a Lie group $G$ with Lie algebra $\mathfrak{g}$ and let $L\mathfrak{g} = C^\infty(S^1, \mathfrak{g})$ the Lie algebra of the loop group $LG$. My question is about continuous Lie algebr …
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Non-invariant forms on loop Lie algebra of semisimple Lie group

Thanks to Yves Cornulier, for suggesting to look at the paper of Neeb and Wagemann. After reading Example 6.2 of that paper (arxiv version), I think the answer to my question is that in fact all 2-cyc …
Matthias Ludewig's user avatar