W*-Superrigidity for cocycle twisted group von Neumann algebras

• 成果类型: Article
• 署名作者: Donvil, Milan; Vaes, Stefaan
• 署名单位: KU Leuven
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01320-5
• 发表日期: 2025
• 页码: 193-260
• 关键词: ii1 factors; PRODUCTS

摘要

We construct countable groups G with the following new degree of W*-superrigidity: if L(G) is virtually isomorphic, in the sense of admitting a bifinite bimodule, with any other group von Neumann algebra L(Lambda), then the groups G and Lambda must be virtually isomorphic. Moreover, we allow both group von Neumann algebras to be twisted by an arbitrary 2-cocycle. We also give examples of II1 factors N that are indecomposable in every sense: they are not virtually isomorphic to any cocycle twisted groupoid von Neumann algebra.