Exercise 2, § 3

Let g be a Lie algebra, $\rho$ a representation of g on a K-module M and $\sigma$ the associated representation of g on $Q = \mathscr{L}(M, M; M)$. For $f \in Q$ to be invariant under $\sigma$, it is necessary and sufficient that the $\rho(x)$ be derivations of M with the multiplication defined by $f$.