For a complex simple Lie algebra $\mathfrak g$ let $\hat{\mathfrak g}$ be its affine Lie algebra (see e.g. http://en.wikipedia.org/wiki/Affine_Lie_algebra#Definition for the definition). Is there an intrinsic way of recovering $\mathfrak g$ from $\hat{\mathfrak g}$? In other words, if I'm given an arbitrarily defined infinite-dimensional Lie algebra $\mathfrak h$ and I know it's isomorphic to $\hat{\mathfrak g}$ for some $\mathfrak g$, is there some deterministic method of finding $\mathfrak g$?

Thanks!

For a complex simple Lie algebra $\mathfrak g$ let $\hat{\mathfrak g}$ be its affine Lie algebra (see e.g. http://en.wikipedia.org/wiki/Affine_Lie_algebra#Definition for the definition). Is there an intrinsic way of recovering $\mathfrak g$ from $\hat{\mathfrak g}$? In other words, if I'm given an arbitrarily defined infinite-dimensional Lie algebra $\mathfrak h$ and I want to know if it's isomorphic to $\hat{\mathfrak g}$ for some $\mathfrak g$, is there some deterministic method of finding what $\mathfrak g$ would have to be?

Thanks!