Lie Groups Beyond an Introduction
《Lie Groups Beyond an Introduction》 · 第 150 页 · Chapter II，Section 5「Abstract Root Systems」
An abstract root system $\Delta$ is said to be reducible if $\Delta$ admits a nontrivial disjoint decomposition $\Delta=\Delta'\cup\Delta''$ with every member of $\Delta'$ orthogonal to every member of $\Delta''$. We say that $\Delta$ is irreducible if it admits no such nontrivial decomposition.