Fixed-point-free fusion automorphisms

2023/06/02 by Schopieray, Andrew
#FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2306.01666

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.

Related

• Automorphisms of fusion systems of finite simple groups of Lie type
• Interpolated family of non-group-like simple integral fusion rings of Lie type
• Burnside type results for fusion categories
• A note on fixed point free automorphisms of groups related to finite fields
• On fusion categories