Normalizer of a Lie subalgebra
= Normalizer of a Lie subalgebra
{title2=$N_L(H)$}
The normalizer of a <Lie subalgebra> $H\subseteq L$ is
$$
N_L(H)=\{x\in L:[x,H]\subseteq H\}.
$$
It is the largest Lie subalgebra of $L$ in which $H$ is an <ideal of a Lie algebra>.