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arXiv · 2306.01666

Fixed-point-free fusion automorphisms

Andrew Schopieray
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Abstract

This is a study of fusion ring automorphisms leaving only the trivial element fixed. We prove that a variety of classical results on fixed-point-free automorphisms of finite groups are true in the generality of fusion rings. As a result, we show there are $8$ Grothendieck equivalence classes of fusion categories of rank less than $9$ with a fixed-point-free fusion automorphism of prime order, generalizing existing results about modular fusion categories of odd dimension.

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Andrew Schopieray. 2023-06-02. Fixed-point-free fusion automorphisms. https://arxiv.org/abs/2306.01666

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