Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of actions of discrete amenable groups on strongly
  amenable subfactors of type III$\lambda$   Using the continuous decomposition, we classify strongly free actions of
discrete amenable groups on strongly amenable subfactors of type III$_\lambda,
0 < \lambda < 1$. Winsl{\o}w's fundamental homomorphism is a complete
invariant. This removes the extra assumptions in the classification theorems of
Loi and Winsl{\o}w and gives a complete classification up to cocycle conjugacy.

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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph