Anomalous Actions of Groups on Tensor Categories
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918017005256704 |
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| author | Lanier, Noah |
| author_facet | Lanier, Noah |
| contents | For a group $G$ and a 4-cocycle $π\in Z^{4}(G,\mathbb{k}^{\times})$, a $π$-anomalous action of $G$ on a linear monoidal category $C$ is a linear monoidal 2-functor between 3-groups $3\text{-Gr}(G,π)\rightarrow \text{2-Aut}_\otimes(C)$ where the latter denotes the 3-group of autoequivalences of $C$. Given $G$ and $π$, we provide a method of constructing anomalous actions of $3\text{-Gr}(G,π)$ on a tensor categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01826 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anomalous Actions of Groups on Tensor Categories Lanier, Noah Quantum Algebra Category Theory For a group $G$ and a 4-cocycle $π\in Z^{4}(G,\mathbb{k}^{\times})$, a $π$-anomalous action of $G$ on a linear monoidal category $C$ is a linear monoidal 2-functor between 3-groups $3\text{-Gr}(G,π)\rightarrow \text{2-Aut}_\otimes(C)$ where the latter denotes the 3-group of autoequivalences of $C$. Given $G$ and $π$, we provide a method of constructing anomalous actions of $3\text{-Gr}(G,π)$ on a tensor categories. |
| title | Anomalous Actions of Groups on Tensor Categories |
| topic | Quantum Algebra Category Theory |
| url | https://arxiv.org/abs/2505.01826 |