Vol. 282, No. 1, 2016

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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