The Brauer-Picard groups of the fusion categories coming from the ADE subfactors

2017/09/14 by Edie-Michell, Cain
#18D10 #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1709.04721

Abstract

We compute the group of Morita auto-equivalences of the even parts of the ADE subfactors, and Galois conjugates. To achieve this we study the braided auto-equivalences of the Drinfeld centres of these categories. We give planar algebra presentations for each of these Drinfeld centres, which we leverage to obtain information about the braided auto-equivalences of the corresponding categories. We also perform the same calculations for the fusion categories constructed from the full ADE subfactors. Of particular interest, the even part of the D₁₀ subfactor is shown to have Brauer-Picard group S₃ × S₃. We develop combinatorial arguments to compute the underlying algebra objects of these invertible bimodules.

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