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arXiv · 2305.14542

Classification of low-rank odd-dimensional modular categories

Agustina Czenky·William Gvozdjak·Julia Plavnik
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Abstract

We prove that any odd-dimensional modular category of rank at most 23 is pointed. We also show that an odd-dimensional modular category of rank 25 is either pointed, perfect, or equivalent to $\operatorname{Rep}(D^\omega(\mathbb Z_7\rtimes \mathbb Z_3))$. Finally, we give partial classification results for modular categories of rank up to 73.

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Agustina Czenky, William Gvozdjak, Julia Plavnik. 2023-05-23. Classification of low-rank odd-dimensional modular categories. https://arxiv.org/abs/2305.14542

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