= Bn Dynkin diagram and affine extension
{c}
For $n\ge2$, the <Bn root system> has <simple roots> $\alpha_i=\varepsilon_i-\varepsilon_{i+1}$ for $i<n$ and $\alpha_n=\varepsilon_n$. Its <Dynkin diagram> is a chain with a double terminal bond pointing toward short $\alpha_n$. The <highest root> is $\theta=\varepsilon_1+\varepsilon_2$. In the <Extended Dynkin diagram>, $\alpha_0=-\theta$ attaches by a single bond to $\alpha_2$ for $n\ge3$. For $n=2$, both long nodes $0,1$ attach by double bonds to short node $2$. Rank one is the <rank-one root system>; its affine diagram has two equal-length nodes joined by a double bond without a short-root arrow.
Back to article page
