Preprojective roots of Coxeter groups

Mark Kleiner

Abstract: For a fixed Coxeter element of a Coxeter group, we introduce the notion of preprojective root that is analogous to the notion of indecomposable preprojective representation of a finite acyclic quiver. We prove that a Coxeter group is finite if and only if each positive root is preprojective.

ArXiv: 1701.02846