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arXiv · 1401.1879

Pseudo-unitary non-self-dual fusion categories of rank 4

Hannah K. Larson
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Abstract

A fusion category of rank $4$ has either four self-dual objects or exactly two self-dual objects. We study fusion categories of rank $4$ with exactly two self-dual objects, giving nearly a complete classification of those based ring that admit pseudo-unitary categorification. More precisely, we show that if $\mathcal{C}$ is such a fusion category, then its Grothendieck ring $K(\mathcal{C})$ must be one of seven based rings, six of which have know categorifications. In doing so, we classify all based rings associated with near-group categories of the group $\mathbb{Z}/3\mathbb{Z}$.

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Hannah K. Larson. 2014-01-09. Pseudo-unitary non-self-dual fusion categories of rank 4. https://arxiv.org/abs/1401.1879

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