Lie Groups Beyond an Introduction
《Lie Groups Beyond an Introduction》 · 第 29 页 · Chapter I, Section 1「Definitions and Examples」，Example 14「Normalizers」
If $\mathfrak g$ is a Lie algebra and $\mathfrak s$ is a Lie subalgebra of $\mathfrak g$, then $N_{\mathfrak g}(\mathfrak s)=\{X\in\mathfrak g\mid[X,Y]\in\mathfrak s\text{ for all }Y\in\mathfrak s\}$ is the normalizer of $\mathfrak s$ in $\mathfrak g$. This is a Lie subalgebra of $\mathfrak g$.