Introduction to Representation Theory
《Introduction to Representation Theory》 · 印刷第 8 页 Section 2.2 的域约定、第 35 页 Section 2.12「The tensor algebra」的张量代数记号及 Definition 2.12.1(iii)（省略中间内容）
Let $k$ be a field. Unless stated otherwise, we will always assume that $k$ is algebraically closed, i.e., any nonconstant polynomial with coefficients in $k$ has a root in $k$. […] Namely, given a vector space $V$, define its tensor algebra $TV$ over a field $k$ to be $TV=\bigoplus_{n\geq 0}V^{\otimes n}$, with multiplication defined by $a\cdot b:=a\otimes b$, $a\in V^{\otimes n}$, $b\in V^{\otimes m}$. […] (iii) If $V$ is a Lie algebra, the universal enveloping algebra $\mathcal U(V)$ of $V$ is the quotient of $TV$ by the ideal generated by $v\otimes w-w\otimes v-[v,w]$, $v,w\in V$.