Vol. 13, No. 1, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 2, 309–612
Issue 1, 1–308

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Absence of Cartan subalgebras for right-angled Hecke von Neumann algebras

Martijn Caspers

Vol. 13 (2020), No. 1, 1–28

For a right-angled Coxeter system (W,S) and q > 0, let q be the associated Hecke von Neumann algebra, which is generated by self-adjoint operators Ts, s S, satisfying the Hecke relation (qTsq)(qTs+1) = 0, as well as suitable commutation relations. Under the assumption that (W,S) is irreducible and |S| 3 it was proved by Garncarek (J. Funct. Anal. 270:3 (2016), 1202–1219) that q is a factor (of type II1) for a range q [ρ,ρ1] and otherwise q is the direct sum of a II1-factor and .

In this paper we prove (under the same natural conditions as Garncarek) that q is noninjective, that it has the weak- completely contractive approximation property and that it has the Haagerup property. In the hyperbolic factorial case q is a strongly solid algebra and consequently q cannot have a Cartan subalgebra. In the general case q need not be strongly solid. However, we give examples of nonhyperbolic right-angled Coxeter groups such that q does not possess a Cartan subalgebra.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Hecke von Neumann algebras, approximation properties, Cartan subalgebras
Mathematical Subject Classification 2010
Primary: 47L10
Received: 10 November 2016
Revised: 2 May 2018
Accepted: 12 February 2019
Published: 6 January 2020
Martijn Caspers
Utrecht University