Class Field Theory
《Class Field Theory》 · 第 77–78 页 · Section 4.1「Representations」，Definition 4.1（省略实表示的平行定义）
Let $G$ be a matrix Lie group. A finite-dimensional complex representation of $G$ is a Lie group homomorphism $\Pi:G\to GL(V)$, where $V$ is a finite-dimensional complex vector space (with $\dim(V)\ge1$). […] If $\mathfrak g$ is a real or complex Lie algebra, then a finite-dimensional complex representation of $\mathfrak g$ is a Lie algebra homomorphism $\pi$ of $\mathfrak g$ into $\mathfrak{gl}(V)$, where $V$ is a finite-dimensional complex vector space. […] If $\Pi$ or $\pi$ is a one-to-one homomorphism, the representation is called faithful.