Modular fusion categories with few twists

Schopieray, Andrew

doi:10.5802/art.36

Schopieray, Andrew

Annals of Representation Theory, Volume 3 (2026) no. 1, pp. 113-140

Abstract

We classify modular fusion categories up to braided equivalence with less than four distinct twists of simple objects by observing that under this assumption, for each positive integer $N$, there are finitely many modular fusion categories of Frobenius–Schur exponent $N$ up to braided equivalence whose twists are a proper subset of the $N^{\mathrm{th}}$ roots of unity.

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Cite this article

Received: 2025-09-06
Revised: 2026-03-05
Accepted: 2026-03-24
Published online: 2026-05-11

DOI: 10.5802/art.36

Classification: 18M20
Keywords: Fusion categories, modular tensor categories

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CC-BY 4.0

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Schopieray, Andrew. Modular fusion categories with few twists. Annals of Representation Theory, Volume 3 (2026) no. 1, pp. 113-140. doi: 10.5802/art.36

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