general linear Lie algebra

《Introduction to Representation Theory》 · 第 22 页 · Section 2.9「Lie algebras」，Example 2.9.2(2)

Any associative algebra $A$ with $[a,b]=ab-ba$, in particular, the endomorphism algebra $A=\operatorname{End}(V)$, where $V$ is a vector space. When such an $A$ is regarded as a Lie algebra, it is often denoted by $\mathfrak{gl}(V)$ (general linear Lie algebra).