Introduction to Lie Algebras and Representation Theory
《Introduction to Lie Algebras and Representation Theory》 · 第 1 页 · Section 1.1「The notion of Lie algebra」
We say that two Lie algebras $L,L'$ over $F$ are isomorphic if there exists a vector space isomorphism $\phi:L\to L'$ satisfying $\phi([xy])=[\phi(x)\phi(y)]$ for all $x,y$ in $L$ (and then $\phi$ is called an isomorphism of Lie algebras).