Class Field Theory
《Class Field Theory》 · 第 54 页 · Section 3.2「Simple, Solvable, and Nilpotent Lie Algebras」，Definition 3.13
Definition 3.13. If $\mathfrak g$ is a Lie algebra, then the commutator ideal in $\mathfrak g$, denoted $[\mathfrak g,\mathfrak g]$, is the space of linear combinations of commutators, that is, the space of elements $Z$ in $\mathfrak g$ that can be expressed as $Z=c_1[X_1,Y_1]+\cdots+c_m[X_m,Y_m]$ for some constants $c_j$ and vectors $X_j,Y_j\in\mathfrak g$.