Quantum symmetries of noncommutative tori

2024/04/22 by David Evans, Evans, David E., Corey Jones +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #Quantum Mechanics and Non-Hermitian Physics

paper · doi:10.48550/arxiv.2404.14466

openalex publication_date 2024/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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 E₈ subfactor on a noncommutative 3-torus, and of PSU(2)₁₅ on a noncommutative 4-torus.

Cited by

• Properly Outer Actions of Tensor Categories on C^*-algebras
• Weak Hopf algebra actions as fusion category actions

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