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.

15 pages, 5 figures

Cited by in corpus (4)

• Absence of Cartan subalgebras for right-angled Hecke von Neumann algebras
• On MASAs in $q$-deformed von Neumann algebras
• Simplicity of right-angled Hecke C${}^{\ast }$-algebras
• On the centre of Iwahori-Hecke algebras