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Let $M$ be a full $\mathrm{II}_1$ factor. Consider mixing and weak mixing subfactors $B$ and $C$ of $M$. Are $B$ and $C$ full?

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    $\begingroup$ Can you give examples of $B$, $C$ and $M$ where this does hold? What is the simplest example of an $M$ where you do not know the answer? $\endgroup$
    – Yemon Choi
    Commented Nov 28, 2019 at 15:14
  • $\begingroup$ See this paper arxiv.org/abs/1001.0169 $\endgroup$
    – sibani
    Commented Nov 28, 2019 at 16:45
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    $\begingroup$ No, I asked if you can give details in your question, rather than expecting other people to do all the work. Your comment also does not provide any reference to a particular section or result of the Cameron-Fang-Mukherjee paper $\endgroup$
    – Yemon Choi
    Commented Nov 28, 2019 at 19:16

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