The set of derivations of an algebra $\Bbb A$ forms a Lie algebra. This is one aspect of why Lie algebras are interesting. When $\Bbb A$ is polynomial algebra in $n$ variable then $\text{Der } \Bbb A$ is well studied. For example, these Lie algebras are infinite-dimensional simple. These include Witt's algebra as a particular case. Witts algebras and Kac-Moody Lie algebras have some similarities I think.

So I was wondering, are there any algebra $\Bbb A$ for which $\text{Der }\Bbb A$ is a Kac-Moody Lie algebra? The question is vague but wants to explore this direction. Kindly share some thoughts or references. Thank you.



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