Introduction to Lie Algebras and Representation Theory
《Introduction to Lie Algebras and Representation Theory》 · 第 10 页 · Section 3.1「Solvability」
It is natural to study a Lie algebra $L$ via its ideals. In this section we exploit the formation of derived algebras. First, define a sequence of ideals of $L$ (the derived series) by $L^{(0)}=L$, $L^{(1)}=[LL]$, $L^{(2)}=[L^{(1)}L^{(1)}]$, $\ldots$, $L^{(i)}=[L^{(i-1)}L^{(i-1)}]$. Call $L$ solvable if $L^{(n)}=0$ for some $n$.