Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Concrete Classification and Centralizers of Certain $\mathbb{Z}^2
  \rtimes {\rm SL}(2,\mathbb{Z})$-actions   We introduce a new class of actions of the group $\G$ on finite von Neumann
algebras and call them twisted Bernoulli shift actions. We classify these
actions up to conjugacy and give an explicit description of their centralizers.
We also distinguish many of those actions on the AFD $\mathrm{II}_1$ factor in
view of outer conjugacy.

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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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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: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci