Q-system completion for C* 2-categories
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866915704905662464 |
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| author | Chen, Quan Palomares, Roberto Hernández Jones, Corey Penneys, David |
| author_facet | Chen, Quan Palomares, Roberto Hernández Jones, Corey Penneys, David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_12010 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Q-system completion for C* 2-categories Chen, Quan Palomares, Roberto Hernández Jones, Corey Penneys, David Operator Algebras Category Theory Quantum Algebra 46L37, 46M15 (primary), 18M20, 18M30, 18N10 (secondary) 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. |
| title | Q-system completion for C* 2-categories |
| topic | Operator Algebras Category Theory Quantum Algebra 46L37, 46M15 (primary), 18M20, 18M30, 18N10 (secondary) |
| url | https://arxiv.org/abs/2105.12010 |