D3 root system
= D3 root system
{c}
{title2=$D_3$}
The $D_3$ roots are $\pm\varepsilon_i\pm\varepsilon_j$ for $1\leq i<j\leq3$. The simple roots
$$
\alpha_1=\varepsilon_1-\varepsilon_2,\quad
\alpha_2=\varepsilon_2-\varepsilon_3,\quad
\alpha_3=\varepsilon_2+\varepsilon_3
$$
form the three-node chain $\alpha_2-\alpha_1-\alpha_3$, so $D_3\cong A_3$.