and the Weyl groups of infinite-dimensional Kac-Moody algebras.

Definition

Formally, a Coxeter group can be defined as a group with the presentation

where and is either an integer or for . Here, the condition means that no relation of the form for any integer should be imposed.

The pair where is a Coxeter group with generators is called a Coxeter system. Note that in general is not uniquely determined