Vol. 13, No. 1, 2020

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

Volume 14
Issue 6, 1671–1976
Issue 5, 1333–1669
Issue 4, 985–1332
Issue 3, 667–984
Issue 2, 323–666
Issue 1, 1–322

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
Subscriptions
 
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
Abstract

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

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/apde

We have not been able to recognize your IP address 34.207.230.188 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:

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