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Title: Quantum Symmetries of Noncommutative Tori
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$$E_{8}$$ E 8 subfactor on a noncommutative 3-torus, and of$$\text {PSU}(2)_{15}$$ PSU ( 2 ) 15 on a noncommutative 4-torus.  more » « less
Award ID(s):
2247202
PAR ID:
10597917
Author(s) / Creator(s):
;
Publisher / Repository:
Springer Science + Business Media
Date Published:
Journal Name:
Communications in Mathematical Physics
Volume:
406
Issue:
7
ISSN:
0010-3616
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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