Unitary conjugacy for type III subfactors and W-superrigidity

  • Yusuke Isono

    Kyoto University, Japan
Unitary conjugacy for type III subfactors and W$^*$-superrigidity cover
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Abstract

Let be inclusions of -finite von Neumann algebras such that and are images of faithful normal conditional expectations. In this article, we investigate Popa's intertwining condition using modular actions on , , and . In the main theorem, we prove that if , then an intertwining element for also intertwines some modular flows of and . As a result, we deduce a new characterization of in terms of the continuous cores of , , and . 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.

Cite this article

Yusuke Isono, Unitary conjugacy for type III subfactors and W-superrigidity. J. Eur. Math. Soc. 24 (2022), no. 5, pp. 1679–1721

DOI 10.4171/JEMS/1135