Quantum groups and generalized circular elements

Michael Brannan, Kay Kirkpatrick

Research output: Contribution to journalArticlepeer-review


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 almostperiodic free Araki-Woods factors.

Original languageEnglish (US)
Pages (from-to)35-61
Number of pages27
JournalPacific Journal of Mathematics
Issue number1
StatePublished - 2016


  • Free araki-woods factor
  • Free probability
  • Free quasifree state
  • Quantum groups

ASJC Scopus subject areas

  • General Mathematics


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