Dynkin diagram

In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line). The multiple edges are, within certain constraints, directed.

The main interest in Dynkin diagrams are as a means to classify semisimple Lie algebras over algebraically closed fields. This gives rise to Weyl groups, i.e. to many (although not all) finite reflection groups. Dynkin diagrams may also arise in other contexts.

The term "Dynkin diagram" can be ambiguous. In some cases, Dynkin diagrams are assumed to be directed, in which case they correspond to root systems and semi-simple Lie algebras, while in other cases they are assumed to be undirected, in which case they correspond to Weyl groups; the ${\displaystyle B_{n}}$ and ${\displaystyle C_{n}}$ directed diagrams yield the same undirected diagram, correspondingly named ${\displaystyle BC_{n}.}$ In this article, "Dynkin diagram" means directed Dynkin diagram, and undirected Dynkin diagrams will be explicitly so named.

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