Putting the Brauer back in Brauer-Picard
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
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| _version_ | 1866917401989218304 |
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| author | Sanford, Sean |
| author_facet | Sanford, Sean |
| contents | We establish a 6-term left exact sequence, involving Galois cohomology of the base field $\mathbb K$, and the Brauer-Picard groupoid of a fusion category. This generalizes a result of Etingof, Nikshych, and Ostrik to the setting where $\mathbb K$ is not algebraically closed. Following their example, we use this exact sequence to compute examples of graded extensions of fusion categories over $\mathbb R$. Along the way, we establish several structural theorems regarding the duality morphisms for a fusion category as an object in the 4-category of braided tensor categories. The paper ends with a speculative look at a potential higher categorical explanation of the main result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10869 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Putting the Brauer back in Brauer-Picard Sanford, Sean Quantum Algebra 18M20 We establish a 6-term left exact sequence, involving Galois cohomology of the base field $\mathbb K$, and the Brauer-Picard groupoid of a fusion category. This generalizes a result of Etingof, Nikshych, and Ostrik to the setting where $\mathbb K$ is not algebraically closed. Following their example, we use this exact sequence to compute examples of graded extensions of fusion categories over $\mathbb R$. Along the way, we establish several structural theorems regarding the duality morphisms for a fusion category as an object in the 4-category of braided tensor categories. The paper ends with a speculative look at a potential higher categorical explanation of the main result. |
| title | Putting the Brauer back in Brauer-Picard |
| topic | Quantum Algebra 18M20 |
| url | https://arxiv.org/abs/2604.10869 |