Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Brauer-Picard groups of the fusion categories coming from the $ADE$
  subfactors   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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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th