Lie Groups Beyond an Introduction
《Lie Groups Beyond an Introduction》 · 印刷第 2—4 页 Introduction Section 1「Linear Lie Algebra of a Closed Linear Group」，闭线性群约定、式 (0.2) 与式 (0.6) 及其后性质（省略例子与推导）
We shall refer to any closed subgroup of some $GL(n,\mathbb C)$ as a closed linear group. […] For any such group $G$, we can speak of smooth curves in $G$, namely $C^\infty$ curves $c(t)$ into the underlying matrix space whose image is in $G$ for each $t$. […] Let $\mathfrak g=\{c'(0)\mid c:\mathbb R\to G\text{ is a curve with }c(0)=1\text{ that is smooth as a function into matrices}\}$. […] We conclude that $\mathfrak g$ is closed under the Lie bracket operation $[X,Y]=XY-YX$. The Lie bracket operation in (0.6) is linear in each variable and has the properties that (a) $[X,X]=0$ for all $X\in\mathfrak g$ (and hence $[X,Y]=-[Y,X]$) and (b) the Jacobi identity holds: $[[X,Y],Z]+[[Y,Z],X]+[[Z,X],Y]=0$.