|
|||||
|
|
|
|
|
|
|
|
|
Quantum groups and
generalized circular elements
Michael Brannan and Kay Kirkpatrick |
|
Vol. 282 (2016), No. 1, 35–61
|
Abstract |
|
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. |
Keywords
quantum groups, free probability, free Araki–Woods factor,
free quasifree state
|
Mathematical Subject Classification 2010
Primary: 20G42, 46L54
Secondary: 46L65
|
Milestones
Received: 19 June 2015
Accepted: 24 August 2015
Published: 24 February 2016
|
Authors |
| 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 |
|
|
