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• W2912644609 abstract "Let $A,Bsubset M$ be inclusions of $sigma$-finite von Neumann algebras such that $A$ and $B$ are images of faithful normal conditional expectations. In this article, we investigate Popa's intertwining condition $Apreceq_MB$ using their modular actions. In the main theorem, we prove that if $Apreceq_MB$ holds, then an intertwining element for $Apreceq_MB$ also intertwines some modular flows of $A$ and $B$. As a result, we deduce a new characterization of $Apreceq_MB$ in terms of their continuous cores. Using this new characterization, we prove the first W$^*$-superrigidity type result for group actions on amenable factors. As another application, we characterize stable strong solidity for free product factors in terms of their free product components." @default.
• W2912644609 created "2019-02-21" @default.
• W2912644609 creator A5020266301 @default.
• W2912644609 date "2019-02-04" @default.
• W2912644609 modified "2023-09-27" @default.
• W2912644609 title "Unitary conjugacy for type III subfactors and W$^*$-superrigidity." @default.
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