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arXiv · 1502.02016

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

Łukasz Garncarek
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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.

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BibTeXRIS

Łukasz Garncarek. 2015-02-06. Factoriality of Hecke-von Neumann algebras of right-angled Coxeter groups. https://doi.org/10.1016/j.jfa.2015.11.014

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