Weak mixing for locally compact quantum groups

Abstract

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 noncommutative Jacobs-de Leeuw-Glicksberg splitting theorem of Runde and the author ["Ergodic theory for quantum semigroups", J. Lond. Math. Soc. (2) 89 (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.

24 pages; v3: minor changes; to appear in Ergodic Theory and Dynamical Systems

References in corpus (6)

• The Haagerup property for locally compact quantum groups
• Bergelson's Theorem for weakly mixing C*-dynamical systems
• Remarks on the Quantum Bohr Compactification
• Relative ergodic properties of C*-dynamical systems
• Ergodic theory for quantum semigroups
• Quantum Eberlein compactifications and invariant means

Cited by in corpus (3)

• Around Property (T) for quantum groups
• Admissibility Conjecture and Kazhdan's Property (T) for quantum groups
• Quantum groups, property (T), and weak mixing