Remarks on symmetric fusion categories of low rank in positive characteristic

2022/11/24 by Agustina Czenky, Czenky, Agustina · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2211.13631

Abstract

We give lower bounds for the rank of a symmetric fusion category in characteristic p≥ 5 in terms of p. We prove that the second Adams operation ψ₂ is not the identity for any non-trivial symmetric fusion category, and that symmetric fusion categories satisfying ψ₂^a=ψ₂^a-1 for some positive integer a are super Tannakian. As an application, we classify all symmetric fusion categories of rank 3 and those of rank 4 with exactly two self dual simple objects.

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