Property (T) discrete quantum groups and subfactors with triangle presentations
Abstract
Kazhdan's property (T) has been studied for several discrete grouplike structures, including standard invariants of Jones' subfactors and discrete quantum groups. We prove a Zuktype 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 directly related to a discrete group with property (T).
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1804.04006
 Bibcode:
 2018arXiv180404006V
 Keywords:

 Mathematics  Operator Algebras;
 Mathematics  Group Theory;
 Mathematics  Quantum Algebra
 EPrint:
 v2: Minor changes, final version, to appear in Advances in Mathematics