Anomalous Actions of Groups on Tensor Categories

Noah Lanier

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arXiv · 2505.01826

Anomalous Actions of Groups on Tensor Categories

Noah Lanier

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Abstract

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.

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Noah Lanier. 2025-05-12. Anomalous Actions of Groups on Tensor Categories. https://arxiv.org/abs/2505.01826

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