Dynkin Diagram

In the mathematical field of Lie theory, a Dynkin diagram is a type of graph with some edges doubled or tripled (drawn as a double or triple line), and with any multiple edges directed, satisfying certain constraints. They are of interest firstly because they classify semisimple Lie algebras over algebraically closed fields, and give rise to Weyl groups, which are many (but not all) of the finite reflection groups. They also arise in other contexts. They are named for Eugene Dynkin; see history, below.

There is ambiguity in the terminology: in some cases Dynkin diagrams are assumed directed, in which case they correspond to root systems and semisimple Lie algebras, while in other cases they are assumed undirected, in which case they correspond to Weyl groups; the and directed diagrams yield the same undirected diagram, correspondingly named In this article, "Dynkin diagram" means directed Dynkin diagram, and undirected Dynkin diagrams will be explicitly so named.