Rank-one root system
= Rank-one root system
{title2=$A_1$}
= A1 root system
{c}
{synonym}
A reduced <root system> of rank one is $Φ=\{\alpha,-\alpha\}$. Its <fundamental weight> is $\alpha/2$, and its <Weyl group> has two elements. Its ordinary <Dynkin diagram> has one node; adjoining $\alpha_0=-\alpha$ gives affine <Cartan matrix> $\begin{pmatrix}2&-2\\-2&2\end{pmatrix}$, drawn as a double bond between equal-length roots.