On cohomology groups of current Lie algebras

In this work we state a result that relates the cohomology groups of a Lie algebra $\frak g$ and a current Lie algebra $\frak g \otimes \mathcal{S}$, by means of a short exact sequence similar to the universal coefficients theorem for modules, where $\mathcal{S}$ is a finite dimensional, commutative and associative algebra with unit over a field $\Bbb F$. Using this result we determine the cohomology group of $\frak g \otimes \mathcal{S}$ where $\frak g$ is a semisimple Lie algebra.