Quantum groups and generalized circular elements

Michael Brannan, Kay Kirkpatrick

Research output: Contribution to journalArticle

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 almostperiodic free Araki-Woods factors.

Original languageEnglish (US)
Pages (from-to)35-61
Number of pages27
JournalPacific Journal of Mathematics
Volume282
Issue number1
DOIs
StatePublished - Jan 1 2016

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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