Examples
There are many examples of groups with the Haagerup property, most of which are geometric in origin. The list includes:
- All compact groups (trivially). Note all compact groups also have property (T). The converse holds as well: if a group has both property (T) and the Haagerup property, then it is compact.
- SO(n,1)
- SU(n,1)
- Groups acting properly on trees or on -trees
- Coxeter groups
- Amenable groups
- Groups acting properly on CAT(0) cubical complexes
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