Let $V$ be a finite-dimensional vector space with $\text{dim}(V) = \ell +1$. Let $\mathfrak{sl}(V)$ be the set of endomorphisms of $V$ with trace equal to zero. Since $\text{Tr}(xy)= \text{Tr}(yx)$ and $\text{Tr}(x+y) =\text{Tr}(x)+\text{Tr}(y)$, $\mathfrak{sl}(V)$ is a subalgebra of the general linear algebra $\mathfrak{gl}(V)$.
Wikidata ID: Q7574831