Remarks on Symmetric Fusion Categories of Low Rank in Positive Characteristic

Author:

Czenky Agustina1

Affiliation:

1. Department of Mathematics, University of Oregon , Eugene, OR 97403, USA

Abstract

Abstract We give lower bounds for the rank of a symmetric fusion category in characteristic $p\geq 5$ in terms of $p$. We prove that the second Adams operation $\psi _{2}$ is not the identity for any non-trivial symmetric fusion category, and that symmetric fusion categories satisfying $\psi _{2}^{a}=\psi _{2}^{a-1}$ 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.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Reference19 articles.

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2. Spherical categories;Barrett;Adv. Math.,1999

3. Cyclotomic integers, fusion categories, and subfactors;Calegari;Comm. Math. Phys.,2011

4. Catégories tannakiennes;Deligne,1990

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