K-theoretic classification of inductive limit actions of fusion categories on AF-algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912800987676672 |
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| author | Chen, Quan Palomares, Roberto Hernández Jones, Corey |
| author_facet | Chen, Quan Palomares, Roberto Hernández Jones, Corey |
| contents | We introduce a K-theoretic invariant for actions of unitary fusion categories on unital C*-algebras. We show that for inductive limits of finite dimensional actions of fusion categories on unital AF-algebras, this is a complete invariant. In particular, this gives a complete invariant for inductive limit actions of finite groups on AF-algebras. We apply our results to obtain a classification of finite depth, strongly AF-inclusions of unital AF-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_11854 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | K-theoretic classification of inductive limit actions of fusion categories on AF-algebras Chen, Quan Palomares, Roberto Hernández Jones, Corey Operator Algebras Quantum Algebra 46L80, 18M20, 46M15 We introduce a K-theoretic invariant for actions of unitary fusion categories on unital C*-algebras. We show that for inductive limits of finite dimensional actions of fusion categories on unital AF-algebras, this is a complete invariant. In particular, this gives a complete invariant for inductive limit actions of finite groups on AF-algebras. We apply our results to obtain a classification of finite depth, strongly AF-inclusions of unital AF-algebras. |
| title | K-theoretic classification of inductive limit actions of fusion categories on AF-algebras |
| topic | Operator Algebras Quantum Algebra 46L80, 18M20, 46M15 |
| url | https://arxiv.org/abs/2207.11854 |