Lie Groups Beyond an Introduction
《Lie Groups Beyond an Introduction》 · 第 30 页 · Chapter I, Section 2「Ideals」
Let $\mathfrak a$ be an ideal in the Lie algebra $\mathfrak g$. Then $\mathfrak g/\mathfrak a$ as a vector space becomes a Lie algebra under the definition $[X+\mathfrak a,Y+\mathfrak a]=[X,Y]+\mathfrak a$ and is called the quotient algebra of $\mathfrak g$ and $\mathfrak a$.