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arXiv · 1903.06345

On slightly degenerate fusion categories

Zhiqiang Yu
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Abstract

In this paper, we first show for a slightly degenerate pre-modular fusion category $\mathcal{C}$ that squares of dimensions of simple objects divide half of the dimension of $\mathcal{C}$, and that slightly degenerate fusion categories of FP-dimensions $2p^nd$ and $4p^nd$ are nilpotent, where $p$ is an odd prime and $d$ is an odd square-free integer. Then we classify slightly degenerate generalized Tambara-Yamagami fusion categories and weakly integral slightly degenerate fusion categories of particular dimensions.

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Zhiqiang Yu. 2019-03-15. On slightly degenerate fusion categories. https://arxiv.org/abs/1903.06345

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