Dynkin diagram

Summary

The Dynkin diagram of a root system is a graph with one vertex for each simple root. The number of edges between two vertices and an arrow record the angle and the length ratio of the two roots. It carries the same information as the Cartan matrix. The connected Dynkin diagrams are the four infinite families $A_n, B_n, C_n, D_n$ and the five exceptional diagrams $E_6, E_7, E_8, F_4, G_2$, and they classify the simple Lie algebras over $\C$.