Tambara-Yamagami Categories over the Reals: The Non-Split Case
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917698517073920 |
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| author | Plavnik, Julia Sanford, Sean Sconce, Dalton |
| author_facet | Plavnik, Julia Sanford, Sean Sconce, Dalton |
| contents | Tambara and Yamagami investigated a simple set of fusion rules with only one non-invertible object, and proved under which circumstances those rules could be given a coherent associator. We consider a generalization of such fusion rules to the setting where simple objects are no longer required to be split simple. Over the real numbers, this means that objects are either real, complex, or quaternionic. In this context, we prove a similar categorification result to the one of Tambara and Yamagami. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17843 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tambara-Yamagami Categories over the Reals: The Non-Split Case Plavnik, Julia Sanford, Sean Sconce, Dalton Quantum Algebra Category Theory 18M20 Tambara and Yamagami investigated a simple set of fusion rules with only one non-invertible object, and proved under which circumstances those rules could be given a coherent associator. We consider a generalization of such fusion rules to the setting where simple objects are no longer required to be split simple. Over the real numbers, this means that objects are either real, complex, or quaternionic. In this context, we prove a similar categorification result to the one of Tambara and Yamagami. |
| title | Tambara-Yamagami Categories over the Reals: The Non-Split Case |
| topic | Quantum Algebra Category Theory 18M20 |
| url | https://arxiv.org/abs/2303.17843 |