Property (T) discrete quantum groups and subfactors with triangle presentations

@article{Vaes2018PropertyD,
  title={Property (T) discrete quantum groups and subfactors with triangle presentations},
  author={S. Vaes and Matthias Valvekens},
  journal={arXiv: Operator Algebras},
  year={2018}
}
Kazhdan's property (T) has been studied for several discrete group-like structures, including standard invariants of Jones' subfactors and discrete quantum groups. We prove a Zuk-type spectral gap criterion for property (T) in this setting. This allows us to construct a family of property (T) discrete quantum groups, as well as subfactor standard invariants, given by generators and a triangle presentation. These are the first examples of property (T) discrete quantum groups that are not… Expand
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