Coxeter element

In mathematics, particularly in the study of reflection groups and Coxeter groups, a **Coxeter element** is a specific type of element that is associated with the generating reflections of a Coxeter group. More formally, a Coxeter group is defined by a set of generators that satisfy certain relations, typically corresponding to reflections across hyperplanes in a geometric space. A Coxeter element is typically constructed by taking a set of generators of the Coxeter group and forming their product in a specific order.