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arXiv · 1803.05568

Reflection fusion categories

Pavel Etingof·César Galindo
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Abstract

We introduce the notion of a $\textit{reflection fusion category}$, which is a type of a $G$-crossed category generated by objects of Frobenius-Perron dimension $1$ and $\sqrt{p}$, where $p$ is an odd prime. We show that such categories correspond to orthogonal reflection groups over $\mathbb{F}_p$. This allows us to use the known classification of irreducible reflection groups over finite fields to classify irreducible reflection fusion categories.

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Pavel Etingof, César Galindo. 2018-03-15. Reflection fusion categories. https://arxiv.org/abs/1803.05568

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