On Étale Algebras and Bosonic Fusion 2-Categories
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913581941915648 |
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| author | Xu, Hao |
| author_facet | Xu, Hao |
| contents | We classify all connected and Lagrangian étale algebras in the Drinfeld center $\mathscr{Z}_1(\mathbf{2Vect}^π_G)$, where $G$ is a finite group and $π$ is a 4-cocycle on $G$. By Décoppet's result every bosonic fusion 2-category $\mathfrak{C}$ has its Drinfeld center equivalent to $\mathscr{Z}_1(\mathbf{2Vect}^π_G)$ for some $G$ and $π$. Combining this fact with classification of Lagrangian algebras in $\mathscr{Z}_1(\mathbf{2Vect}^π_G)$, we obtain a classification of bosonic fusion 2-categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Étale Algebras and Bosonic Fusion 2-Categories Xu, Hao Category Theory 18A50, 18D20, 18D25, 18M05, 18M15, 18M20 (Primary), 18M25, 18M30, 18N10, 18N20, 18N25 We classify all connected and Lagrangian étale algebras in the Drinfeld center $\mathscr{Z}_1(\mathbf{2Vect}^π_G)$, where $G$ is a finite group and $π$ is a 4-cocycle on $G$. By Décoppet's result every bosonic fusion 2-category $\mathfrak{C}$ has its Drinfeld center equivalent to $\mathscr{Z}_1(\mathbf{2Vect}^π_G)$ for some $G$ and $π$. Combining this fact with classification of Lagrangian algebras in $\mathscr{Z}_1(\mathbf{2Vect}^π_G)$, we obtain a classification of bosonic fusion 2-categories. |
| title | On Étale Algebras and Bosonic Fusion 2-Categories |
| topic | Category Theory 18A50, 18D20, 18D25, 18M05, 18M15, 18M20 (Primary), 18M25, 18M30, 18N10, 18N20, 18N25 |
| url | https://arxiv.org/abs/2411.13367 |