Introduction to Lie Algebras and Representation Theory
《Introduction to Lie Algebras and Representation Theory》 · 第 11 页 · Section 3.2「Nilpotency」
The definition of solvability imitates the corresponding notion in group theory, which goes back to Abel and Galois. By contrast, the notion of nilpotent group is more recent, and is modeled on the corresponding notion for Lie algebras. Define a sequence of ideals of $L$ (the descending central series, also called the lower central series) by $L^0=L$, $L^1=[LL]$ $(=L^{(1)})$, $L^2=[LL^1]$, $\ldots$, $L^i=[L\ L^{i-1}]$. $L$ is called nilpotent if $L^n=0$ for some $n$.