Kazhdan's Property T for Discrete Quantum Groups

2008/12/03 by Pierre Fima, Fima, Pierre
Mathematics · #46L10 #46L52 #46L65 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L10 #msc:46L52 #msc:46L65

paper · pdf · doi:10.48550/arxiv.0812.0665

arxiv created 2008/12/03 · arxiv updated 2009/12/01

Abstract

We give a simple definition of property T for discrete quantum groups. We prove the basic expected properties: discrete quantum groups with property T are finitely generated and unimodular. Moreover we show that, for "I.C.C." discrete quantum groups, property T is equivalent to Connes' property T for the dual von Neumann algebra. This allows us to give the first example of a property T discrete quantum group which is not a group using the twisting construction.

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