For a Coxeter group with simple generators 
, ..., 
, a Coxeter element is a product of the simple generators
in some order, such as 
.
In a finite irreducible Coxeter
group (one whose Coxeter-Dynkin diagram
is connected), all Coxeter elements are conjugate
and have the same order, called the Coxeter
number.
Coxeter Element
See also
Coxeter-Dynkin Diagram, Coxeter Group, Coxeter Number, Coxeter PlaneExplore with Wolfram|Alpha
References
Humphreys, J. E. Reflection Groups and Coxeter Groups. Cambridge, England: Cambridge University Press, 1990.Cite this as:
Weisstein, Eric W. "Coxeter Element." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CoxeterElement.html