Introduction to Lie Algebras and Representation Theory
《Introduction to Lie Algebras and Representation Theory》 · 印刷第 90 页 Section 17.2 的对象约定、第 91 页泛包络代数与商映射的构造、第 91—92 页 Section 17.3「PBW Theorem and consequences」的命名句及 Corollary C 完整陈述（省略中间内容）
We begin with the abstract definition, for an arbitrary Lie algebra $L$ (allowed here to be infinite dimensional, contrary to our usual convention). […] Let $\mathfrak T(L)$ be the tensor algebra on $L$ (17.1), and let $J$ be the two sided ideal in $\mathfrak T(L)$ generated by all $x\otimes y-y\otimes x-[xy]$ ($x,y\in L$). Define $\mathfrak U(L)=\mathfrak T(L)/J$, and let $\pi:\mathfrak T(L)\to\mathfrak U(L)$ be the canonical homomorphism. […] The following theorem is the basic result about $\mathfrak U(L)$; it (or its Corollary C) is called the Poincaré-Birkhoff-Witt Theorem (or PBW Theorem). […] Corollary C. Let $(x_1,x_2,x_3,\ldots)$ be any ordered basis of $L$. Then the elements $x_{i(1)}\cdots x_{i(m)}=\pi(x_{i(1)}\otimes\cdots\otimes x_{i(m)})$, $m\in\mathbb Z^+$, $i(1)\leq i(2)\cdots\leq i(m)$, along with $1$, form a basis of $\mathfrak U(L)$.