Property (T) discrete quantum groups and subfactors with triangle presentations
Operator Algebras
2022-10-04 v2 Group Theory
Quantum Algebra
Abstract
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 directly related to a discrete group with property (T).
Cite
@article{arxiv.1804.04006,
title = {Property (T) discrete quantum groups and subfactors with triangle presentations},
author = {Stefaan Vaes and Matthias Valvekens},
journal= {arXiv preprint arXiv:1804.04006},
year = {2022}
}
Comments
v2: Minor changes, final version, to appear in Advances in Mathematics