The Tannakian radical and the mantle of a braided fusion category
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915497657761792 |
|---|---|
| author | Green, Jason Nikshych, Dmitri |
| author_facet | Green, Jason Nikshych, Dmitri |
| contents | We define the Tannakian radical of a braided fusion category $\mathcal{C}$ as the intersection of its maximal Tannakian subcategories. The localization of $\mathcal{C}$ corresponding to the Tannakian radical, termed the mantle of $\mathcal{C}$, admits a canonical central extension that serves as a complete invariant of $\mathcal{C}$. The mantle has a trivial Tannakian radical, and we refer to braided fusion categories with this property as reductive. We investigate the properties and structure of reductive categories and prove several classification results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16722 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Tannakian radical and the mantle of a braided fusion category Green, Jason Nikshych, Dmitri Quantum Algebra Representation Theory We define the Tannakian radical of a braided fusion category $\mathcal{C}$ as the intersection of its maximal Tannakian subcategories. The localization of $\mathcal{C}$ corresponding to the Tannakian radical, termed the mantle of $\mathcal{C}$, admits a canonical central extension that serves as a complete invariant of $\mathcal{C}$. The mantle has a trivial Tannakian radical, and we refer to braided fusion categories with this property as reductive. We investigate the properties and structure of reductive categories and prove several classification results. |
| title | The Tannakian radical and the mantle of a braided fusion category |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2412.16722 |