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arXiv · 1902.01049

Unitary conjugacy for type III subfactors and W$^*$-superrigidity

Yusuke Isono
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Abstract

Let $A,B\subset M$ 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 $A\preceq_MB$ using their modular actions. In the main theorem, we prove that if $A\preceq_MB$ holds, then an intertwining element for $A\preceq_MB$ also intertwines some modular flows of $A$ and $B$. As a result, we deduce a new characterization of $A\preceq_MB$ 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.

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Yusuke Isono. 2019-02-04. Unitary conjugacy for type III subfactors and W$^*$-superrigidity. https://arxiv.org/abs/1902.01049

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