# Weyl's theorem on complete reducibility

In algebra, Weyl's theorem on complete reducibility is a fundamental result in the theory of Lie algebra representations. Let $\mathfrak{g}$ be a semisimple Lie algebra over a field of characteristic zero. The theorem states that every finite-dimensional module over $\mathfrak{g}$ is semisimple as a module (i.e., a direct sum of simple modules.)