# Reference request: Category of finite dimensional representations of loop algebra is not semisimple

For $$\mathfrak{g}$$ a semisimple Lie algebra, we may define its (untwisted) loop algebra as $$L(\mathfrak{g}) = \mathfrak{g} \otimes \mathbb{C}\lbrack t,t^{-1} \rbrack$$. Let $$\mathcal{F}$$ be the category of finite-dimensional $$L(\mathfrak{g})$$-modules.

It is stated throughout the literature (e.g. [1]) that $$\mathcal{F}$$ is not semisimple. While it is straightforward to find an object in $$\mathcal{F}$$ that is reducible but not decomposable, I would like to know whether a purely categorical/algebraic (i.e. abstract) proof of this fact is known?

[1] Senesi, P. 2009. Finite-dimensional Representation Theory of Loop Algebras: A Survey. (https://arxiv.org/abs/0906.0099).