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arXiv · 2511.23123

McDuff superrigidity for group II$_1$ factors

Juan Felipe Ariza Mejía·Ionuţ Chifan·Denis Osin·Bin Sun
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Abstract

Developing new techniques at the interface of geometric group theory and von Neumann algebras, we identify the first examples of ICC groups $G$ whose von Neumann algebras are McDuff and exhibit a new rigidity phenomenon, termed McDuff superrigidity: an arbitrary group $H$ satisfying $\mathcal{L}(H)\cong \mathcal{L}(G)$ decomposes as $H \cong G\times A$ for an ICC amenable group $A$.

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Juan Felipe Ariza Mejía, Ionuţ Chifan, Denis Osin, Bin Sun. 2025-11-28. McDuff superrigidity for group II$_1$ factors. https://arxiv.org/abs/2511.23123

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