W*-superrigidity for discrete quantum groups

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.

v2: minor changes, final version, to appear in Communications in Mathematical Physics

References in corpus (5)

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• W*-rigidity paradigms for embeddings of II${}_1$ factors
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