Introduction to Lie Algebras and Representation Theory
《Introduction to Lie Algebras and Representation Theory》 · 第 4 页 · Section 1.4「Abstract Lie algebras」
For example, if $L$ is an arbitrary finite dimensional vector space over $F$, we can view $L$ as a Lie algebra by setting $[xy]=0$ for all $x,y\in L$. Such an algebra, having trivial Lie multiplication, is called abelian (because in the linear case $[x,y]=0$ just means that $x$ and $y$ commute).