Introduction to Lie Algebras and Representation Theory
《Introduction to Lie Algebras and Representation Theory》 · 第 25 页 · Section 6「Complete reducibility of representations」章首维数约定及 Section 6.1「Modules」的对象约定与等价表示定义（省略中间内容）
In this section all representations are finite dimensional, unless otherwise noted. […] Let $L$ be a Lie algebra. […] A homomorphism of $L$-modules is a linear map $\phi:V\to W$ such that $\phi(x.v)=x.\phi(v)$. […] When $\phi$ is an isomorphism of vector spaces, we call it an isomorphism of $L$-modules; in this case, the two modules are said to afford equivalent representations of $L$.