Second cohomology group of an affine Lie algebra

If $L$ is a finite-dimensional simple Lie algebra (over $mathbb{C}$), then it is apparently the case that $H^2(Lotimesmathbb{C}[t,t^{-1}],mathbb{C})$ ($Lotimesmathbb{C}[t,t^{-1}]$ being the loop algebra of $L$, with Lie bracket $[xotimes f,yotimes g]=[x,y]otimes fg$) is isomorphic to $mathbb{C}$. In the literature that I have looked at I can only find one proof (Conformal Field Theory and Topology – T. Kohno), but this relies on the fact that $L$ is the Lie algebra of a compact Lie group.

My question: is there an algebraic proof, and if so, does someone know or have a good reference that I can use?