Kazhdan's Property T for Discrete Quantum Groups

Pierre Fima (1)

1 Department of Mathematics [Urbana]

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.

Mots clés: Compact quantum groups; Discrete quantum groups; Property T; II1 factors

Domaines: Algèbres d'opérateurs [math.OA]

Pierre Fima. Kazhdan's Property T for Discrete Quantum Groups. 2008. ⟨hal-00343874⟩