Class Field Theory
《Class Field Theory》 · 第 51 页 · Section 3.1「Definitions and First Examples」，Definition 3.7
Definition 3.7. If $\mathfrak g$ is a Lie algebra and $X$ is an element of $\mathfrak g$, define a linear map $\operatorname{ad}_X:\mathfrak g\to\mathfrak g$ by $\operatorname{ad}_X(Y)=[X,Y]$. The map $X\mapsto\operatorname{ad}_X$ is the adjoint map or adjoint representation.