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arXiv · 1709.04721

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

Cain Edie-Michell
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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 $D_{10}$ subfactor is shown to have Brauer-Picard group $S_3 \times S_3$. We develop combinatorial arguments to compute the underlying algebra objects of these invertible bimodules.

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BibTeXRIS

Cain Edie-Michell. 2017-09-14. The Brauer-Picard groups of the fusion categories coming from the $ADE$ subfactors. https://arxiv.org/abs/1709.04721

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