Around Property (T) for Quantum Groups

Matthew Daws, Adam Skalski, Ami Viselter

Research output: Contribution to journalArticlepeer-review


We study Property (T) for locally compact quantum groups, providing several new characterisations, especially related to operator algebraic ergodic theory. Quantum Property (T) is described in terms of the existence of various Kazhdan type pairs, and some earlier structural results of Kyed, Chen and Ng are strengthened and generalised. For second countable discrete unimodular quantum groups with low duals, Property (T) is shown to be equivalent to Property (T)1,1 of Bekka and Valette. This is used to extend to this class of quantum groups classical theorems on ‘typical’ representations (due to Kerr and Pichot), and on connections of Property (T) with spectral gaps (due to Li and Ng) and with strong ergodicity of weakly mixing actions on a particular von Neumann algebra (due to Connes and Weiss). Finally, we discuss in the Appendix equivalent characterisations of the notion of a quantum group morphism with dense image.

Original languageAmerican English
Pages (from-to)69-118
Number of pages50
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - 1 Jul 2017

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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