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タイトル: | Unitary conjugacy for type III subfactors and W*-superrigidity |
著者: | Isono, Yusuke |
著者名の別形: | 磯野, 優介 |
キーワード: | 46L10 46L36 46L55 37A20 W*-superrigidity Popa’s intertwining theory Tomita–Takesaki theory strong solidity |
発行日: | 2022 |
出版者: | European Mathematical Society |
誌名: | Journal of the European Mathematical Society |
巻: | 24 |
号: | 5 |
開始ページ: | 1679 |
終了ページ: | 1721 |
抄録: | Let A, B ⊂ M be inclusions of σ-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 M B using modular actions on A, B, and M. In the main theorem, we prove that if A ⪯M B, then an intertwining element for A ⪯M B also intertwines some modular flows of A and B. As a result, we deduce a new characterization of A ⪯M B in terms of the continuous cores of A, B, and M. 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. |
記述: | This article is published open access under our Subscribe to Open model. |
著作権等: | ©2021 European Mathematical Society Published by EMS Press. This work is licensed under a Creative Commons Attribution 4.0 International license. |
URI: | http://hdl.handle.net/2433/274909 |
DOI(出版社版): | 10.4171/jems/1135 |
出現コレクション: | 学術雑誌掲載論文等 |
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