Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A remark on amenable von Neumann subalgebras in a tracial free product   Let $M=M_1*M_2$ be a nontrivial tracial free product of finite von Neumann
algebras. We prove that any amenable subalgebra of $M$ that has a diffuse
intersection with $M_1$ is in fact contained in $M_1$. This has been proved by
C. Houdayer under more general circumstances.

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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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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: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci