Q-system completion for C⁎ 2-categories

A Q-system in a C⁎ 2-category is a unitary version of a separable Frobenius algebra object and can be viewed as a unitary version of a higher idempotent. We define a higher unitary idempotent completion for C⁎ 2-categories called Q-system completion and study its properties. We show that the C⁎ 2-ca...

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Bibliographic Details
Published in:Journal of functional analysis 2022-08, Vol.283 (3), p.109524, Article 109524
Main Authors: Chen, Quan, Hernández Palomares, Roberto, Jones, Corey, Penneys, David
Format: Article
Language:English
Subjects:
Categories, functors in functional analysis
Fusion categories, modular tensor categories, modular functors
String diagrams and graphical calculi
Subfactor classification
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Summary:A Q-system in a C⁎ 2-category is a unitary version of a separable Frobenius algebra object and can be viewed as a unitary version of a higher idempotent. We define a higher unitary idempotent completion for C⁎ 2-categories called Q-system completion and study its properties. We show that the C⁎ 2-category of right correspondences of unital C⁎-algebras is Q-system complete by constructing an inverse realization †-2-functor. We use this result to construct induced actions of group theoretical unitary fusion categories on continuous trace C⁎-algebras with connected spectra.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2022.109524