Dynkin diagram

A Dynkin diagram is a type of graph, with some edges doubled or tripled and drawn as a double or triple line, named for the mathematician Eugene Dynkin. Dynkin diagrams arise in Lie theory in the classification of semisimple Lie algebras over algebraically closed fields, in the classification of Weyl groups and other finite reflection groups, and in other contexts. A diagram is built from a root system: its vertices are the simple roots, and an edge count of none, one, two or three records whether the angle between two roots is 90, 120, 135 or 150 degrees, with an arrow pointing from the longer root to the shorter. Properties of the diagram, such as whether it has multiple edges or symmetries, correspond to important features of the associated Lie algebra. Dropping the arrows gives the undirected diagram, which is a form of Coxeter diagram and classifies Weyl groups. The index n counts the nodes, which equals the rank of the Lie algebra.