Inclusions of operator algebras from tensor categories: beyond irreducibility

Journal article

We derive faithful inclusions of C*-algebras from a coend-type construction in unitary tensor categories. This gives rise to different potential notions of discreteness for an inclusion in the non-irreducible case and provides a unified framework that encloses the theory of compact quantum group actions. We also provide examples coming from semi-circular systems and from factorization homology. In the irreducible case, we establish conditions under which the C*-discrete and W*-discrete conditions are equivalent.

Authors: Hataishi, L; Palomares, RH

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: Glasgow Mathematical Journal
• Pages: 1-35
• Publication date: 2025-11-03
• Acceptance date: 2025-09-07
• DOI: 10.1017/s0017089525100839
• EISSN: 1469-509X
• ISSN: 0017-0895
• Language: English
• Keywords: 46L05; quantum symetries; Discrete inclusions; unitary tensor categories; 46M15; 46L37