Lie subalgebra

《Introduction to Representation Theory》 · 第 22 页 · Section 2.9「Lie algebras」，Example 2.9.2(5)

Any subspace $\mathfrak a$ of a Lie algebra $\mathfrak g$ which is closed under the commutator map $[\ ,\ ]$, i.e., such that $[a,b]\in\mathfrak a$ if $a,b\in\mathfrak a$. Such a subspace is called a Lie subalgebra of $\mathfrak g$.