Quantum symmetries of noncommutative tori
Quantum Algebra
2025-01-09 v3 Mathematical Physics
math.MP
Operator Algebras
Abstract
We consider the problem of building non-invertible quantum symmetries (as characterized by actions of unitary fusion categories) on noncommutative tori. We introduce a general method to construct actions of fusion categories on inductive limit C*-algberas using finite dimenionsal data, and then apply it to obtain AT-actions of arbitrary Haagerup-Izumi categories on noncommutative 2-tori, of the even part of the subfactor on a noncommutative 3-torus, and of on a noncommutative 4-torus.
Cite
@article{arxiv.2404.14466,
title = {Quantum symmetries of noncommutative tori},
author = {David E. Evans and Corey Jones},
journal= {arXiv preprint arXiv:2404.14466},
year = {2025}
}