Constructs the first examples of separable II₁ factors with no non-trivial crossed product decompositions via a novel embedding property into the tensor square.
W*-superrigidity for discrete quantum groups
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abstract
A discrete group $G$ is called W*-superrigid if the group $G$ can be entirely recovered from the ambient group von Neumann algebra $L(G)$. We introduce an analogous notion for discrete quantum groups. We prove that this strengthened quantum W*-superrigidity property holds for a natural family of co-induced discrete quantum groups. We also prove that, remarkably, most existing families of W*-superrigid groups are not quantum W*-superrigid.
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2026 1verdicts
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A class of II$_1$ factors without non-trivial crossed product decompositions
Constructs the first examples of separable II₁ factors with no non-trivial crossed product decompositions via a novel embedding property into the tensor square.