Kazhdan's Property T for Discrete Quantum Groups

By Pierre Fima. 2008

61 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f0ecc94725f16839a82b10d2c2719e2368053a42

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Matthew Daws
2. Stuart White
3. Adam G. Skalski
4. Pierre Fima

In Geometry and Topology

1. Matthew Daws
2. Stuart White
3. Adam G. Skalski
4. Pierre Fima

In Mathematical Physics

1. Matthew Daws
2. Stuart White
3. Adam G. Skalski
4. Pierre Fima
5. David Kerr

Citations in the corpus

• The Haagerup property for locally compact quantum groups (2013, background): “Recall that a locally compact quantum group has property (T) if each of its representations with almost invariant vectors has a nontrivial invariant vector – this notion was introduced (for discrete quantum groups) in [31] and later studied in [54].”