An Elliott intertwining approach to classifying actions of C$^*$-tensor categories
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911574678044672 |
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| author | Pacheco, Sergio Girón Neagu, Robert |
| author_facet | Pacheco, Sergio Girón Neagu, Robert |
| contents | We introduce a categorical approach to classifying actions of C$^*$-tensor categories $\mathcal{C}$ on C$^*$-algebras up to cocycle conjugacy. We show that, in this category, inductive limits exist and there is a natural notion of approximate unitary equivalence. Then, we generalise classical Elliott intertwining results to the $\mathcal{C}$-equivariant case, in the same fashion as done by Szabó for the group equivariant case in [39]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18125 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Elliott intertwining approach to classifying actions of C$^*$-tensor categories Pacheco, Sergio Girón Neagu, Robert Operator Algebras Quantum Algebra 46L35, 46L37, 46L55, 18D10 We introduce a categorical approach to classifying actions of C$^*$-tensor categories $\mathcal{C}$ on C$^*$-algebras up to cocycle conjugacy. We show that, in this category, inductive limits exist and there is a natural notion of approximate unitary equivalence. Then, we generalise classical Elliott intertwining results to the $\mathcal{C}$-equivariant case, in the same fashion as done by Szabó for the group equivariant case in [39]. |
| title | An Elliott intertwining approach to classifying actions of C$^*$-tensor categories |
| topic | Operator Algebras Quantum Algebra 46L35, 46L37, 46L55, 18D10 |
| url | https://arxiv.org/abs/2310.18125 |