Vol. 282, No. 1, 2016

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 325: 1
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Quantum groups and generalized circular elements

Michael Brannan and Kay Kirkpatrick

Vol. 282 (2016), No. 1, 35–61

We show that with respect to the Haar state, the joint distributions of the generators of Van Daele and Wang’s free orthogonal quantum groups are modeled by free families of generalized circular elements and semicircular elements in the large (quantum) dimension limit. We also show that this class of quantum groups acts naturally as distributional symmetries of almost-periodic free Araki–Woods factors.

quantum groups, free probability, free Araki–Woods factor, free quasifree state
Mathematical Subject Classification 2010
Primary: 20G42, 46L54
Secondary: 46L65
Received: 19 June 2015
Accepted: 24 August 2015
Published: 24 February 2016
Michael Brannan
Department of Mathematics
Texas A&M University
College Station, TX 77843
United States
Kay Kirkpatrick
University of Illinois at Urbana-Champaign
Urbana, IL 61821
United States