A2 root system
= A2 root system
{c}
{title2=$A_2$}
The $A_2$ <root system> has equal-length <simple roots> $\alpha_1,\alpha_2$ with angle $2\pi/3$, and roots $\pm\alpha_1$, $\pm\alpha_2$, $\pm(\alpha_1+\alpha_2)$. Its <Cartan matrix> is $\begin{pmatrix}2&-1\\-1&2\end{pmatrix}$. The corresponding complex <simple Lie algebra> is $\mathfrak{sl}_3(\mathbb C)$, of dimension eight.