Quantum symmetries of noncommutative tori

Evans, David and Jones, Corey 2025. Quantum symmetries of noncommutative tori. Communications in Mathematical Physics 406 , 167. 10.1007/s00220-025-05337-y

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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 subfactor on a noncommutative 3-torus, and of on a noncommutative 4-torus.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Schools > Mathematics
Publisher:	Springer
ISSN:	0010-3616
Date of First Compliant Deposit:	3 June 2025
Date of Acceptance:	28 April 2025
Last Modified:	05 Jun 2025 10:00
URI:	https://orca.cardiff.ac.uk/id/eprint/178700

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