Normalizer of a Lie subalgebra

Summary

The normalizer of a Lie subalgebra $\mathfrak k$ of a Lie algebra $\mathfrak g$ is the set of elements $x$ with $[x, \mathfrak k] \subseteq \mathfrak k$. It is the largest subalgebra of $\mathfrak g$ that contains $\mathfrak k$ as an ideal. It is the Lie algebra analogue of the normaliser of a subgroup. Cartan subalgebras are defined as nilpotent subalgebras that equal their own normalizer.