Weak mixing for locally compact quantum groups

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We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the non-commutative Jacobs-de Leeuw-Glicksberg splitting theorem of Runde and the author [Ergodic theory for quantum semigroups. J. Lond. Math. Soc. (2) 89(3) (2014), 941-959]. Furthermore, a relation between mixing and weak mixing of state-preserving actions of discrete quantum groups and the properties of certain inclusions of von Neumann algebras, which is known for discrete groups, is demonstrated.

Original languageEnglish
Pages (from-to)1657-1680
Number of pages24
JournalErgodic Theory and Dynamical Systems
Issue number5
StatePublished - 1 Aug 2017

Bibliographical note

Publisher Copyright:
© 2016 Cambridge University Press.

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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