Factoriality of Hecke-von Neumann algebras of right-angled Coxeter groups

Abstract

The Hecke algebra $\mathbb{C}_q[W]$ of a Coxter group $W$, associated to parameter $q$, can be completed to a von Neumann algebra $\mathcal{N}_q(W)$. We study such algebras in case where $W$ is right-angled. We determine the range of $q$ for which $\mathcal{N}_q(W)$ is a factor, i.e. has trivial center. Moreover, in case of nontrivial center, we prove a result allowing to decompose $\mathcal{N}_q(W)$ into a finite direct sum of factors.