Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three natural subgroups of the Brauer-Picard group of a Hopf algebra
  with applications   In this article we construct three explicit natural subgroups of the
Brauer-Picard group of the category of representations of a finite-dimensional
Hopf algebra. In examples the Brauer Picard group decomposes into an ordered
product of these subgroups, somewhat similar to a Bruhat decomposition.
  Our construction returns for any Hopf algebra three types of braided
autoequivalences and correspondingly three families of invertible bimodule
categories. This gives examples of so-called (2-)Morita equivalences and
defects in topological field theories. We have a closer look at the case of
quantum groups and Nichols algebras and give interesting applications. Finally,
we briefly discuss the three families of group-theoretic extensions.

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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an