Dynkin Diagrams

reset

menu of Dynkin diagrams:

A1

recognize as type:

finite

affine

hyperbolic

very extended

Coxeter geometric permutation:

1

name:

Parent

This Demonstration lets you create and modify multiple Dynkin and Coxeter–Dynkin diagrams. Some topological patterns can be recognized for a known simple Lie group (up to rank 8) and its designated type, including finite, affine, hyperbolic, and very extended. You can use the dropdown "Dynkin diagrams" to get various diagrams and geometric permutations.

You can also modify, recognize, and name the

rank

2

(binary) Coxter–Dynkin geometric permutations on uniform polyhedra and name their Wythoff construction operator. These permutations are indicated by filled nodes. When more than one diagram is created, they can be interpreted as a geometric Cartesian product, such as a duoprism.

The Cartan matrix that defines the Lie algebra is calculated directly from the last diagram entered.