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arXiv · 2404.14466

Quantum symmetries of noncommutative tori

David E. Evans·Corey Jones
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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 $E_{8}$ subfactor on a noncommutative 3-torus, and of $\text{PSU}(2)_{15}$ on a noncommutative 4-torus.

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BibTeXRIS

David E. Evans, Corey Jones. 2024-04-22. Quantum symmetries of noncommutative tori. https://arxiv.org/abs/2404.14466

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