Remarks on symmetric fusion categories of low rank in positive characteristic
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909264583327744 |
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| author | Czenky, Agustina |
| author_facet | Czenky, Agustina |
| contents | We give lower bounds for the rank of a symmetric fusion category in characteristic $p\geq 5$ in terms of $p$. We prove that the second Adams operation $ψ_2$ is not the identity for any non-trivial symmetric fusion category, and that symmetric fusion categories satisfying $ψ_2^a=ψ_2^{a-1}$ for some positive integer $a$ are super Tannakian. As an application, we classify all symmetric fusion categories of rank 3 and those of rank 4 with exactly two self dual simple objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_13631 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Remarks on symmetric fusion categories of low rank in positive characteristic Czenky, Agustina Quantum Algebra Representation Theory 18M20, 18M25 We give lower bounds for the rank of a symmetric fusion category in characteristic $p\geq 5$ in terms of $p$. We prove that the second Adams operation $ψ_2$ is not the identity for any non-trivial symmetric fusion category, and that symmetric fusion categories satisfying $ψ_2^a=ψ_2^{a-1}$ for some positive integer $a$ are super Tannakian. As an application, we classify all symmetric fusion categories of rank 3 and those of rank 4 with exactly two self dual simple objects. |
| title | Remarks on symmetric fusion categories of low rank in positive characteristic |
| topic | Quantum Algebra Representation Theory 18M20, 18M25 |
| url | https://arxiv.org/abs/2211.13631 |