Actions, Quotients and Lattices of Locally Compact Quantum Groups

Michael Brannan, Alexandru Chirvasitu, Ami Viselter

Research output: Contribution to journalArticlepeer-review


We prove a number of property (T) permanence re-sults for locally compact quantum groups under exact sequences and the presence of invariant states, analogous to their classical versions. Along the way we characterize the existence of invariant weights on quantum homogeneous spaces of quotient type, and relate invariant states for LCQG actions on von Neumann algebras to invariant vec-tors in canonical unitary implementations, providing an application to amenability. Finally, we introduce a notion of lattice in a locally compact quantum group, noting examples provided by Drinfeld doubles of compact quantum groups. We show that property (T) lifts from a lattice to the ambient LCQG, just as it does classically, thus obtaining new examples of non-classical, non-compact, non-discrete LCQGs with property (T).

Original languageEnglish
Pages (from-to)2553-2582
Number of pages30
JournalDocumenta Mathematica
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020, EMS Press. All rights reserved.


  • canonical implementation
  • closed quantum sub-group
  • lattice
  • locally compact quantum group
  • property (T)
  • weight

ASJC Scopus subject areas

  • General Mathematics


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