Editing Dynkin diagram (section)

{{Short description|Pictorial representation of symmetry}}
{{Lie groups |Semi-simple}}

In the [[Mathematics|mathematical]] field of [[Lie theory]], a '''Dynkin diagram''', named for [[Eugene Dynkin]], is a type of [[Graph (discrete mathematics)|graph]] with some edges doubled or tripled (drawn as a double or triple line).  Dynkin diagrams arise in the classification of [[semisimple Lie algebra]]s over [[algebraically closed field]]s, in the classification of [[Weyl group]]s and other [[finite reflection group]]s, and in other contexts.  Various properties of the Dynkin diagram (such as whether it contains multiple edges, or its symmetries) correspond to important features of the associated Lie algebra.

[[File:Finite Dynkin diagrams.svg|thumb|Finite Dynkin diagrams]]
[[File:Affine Dynkin diagrams.png|thumb|Affine (extended) Dynkin diagrams]]

The term "Dynkin diagram" can be ambiguous. In some cases, Dynkin diagrams are assumed to be [[directed graph|directed]], in which case they correspond to [[root system]]s and semi-simple Lie algebras, while in other cases they are assumed to be [[undirected graph|undirected]], in which case they correspond to Weyl groups. In this article, "Dynkin diagram" means ''directed'' Dynkin diagram, and ''undirected'' Dynkin diagrams will be explicitly so named.