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New examples of W∗ and C∗-superrigid groups
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New examples of W∗ and C∗-superrigid groups

Ionut Chifan, Alec Diaz-Arias and Daniel Drimbe
ArXiv.org
Cornell University
11/09/2022
DOI: 10.48550/arxiv.2010.01223
url
https://doi.org/10.1016/j.aim.2022.108797View
Published (Version of record)This article has now been published in a journal and has been peer-reviewed by subject experts. This version may differ significantly from the preprint version. Access restricted to faculty, staff and students
url
https://doi.org/10.48550/arxiv.2010.01223View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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Abstract

A group G is called W∗-superrigid (resp. C∗-superrigid) if it is completely recognizable from its von Neumann algebra L(G) (resp. reduced C∗-algebra C∗r(G)). Developing new technical aspects in Popa's deformation/rigidity theory we introduce several new classes of W∗-superrigid groups which appear as direct products, semidirect products with non-amenable core and iterations of amalgamated free products and HNN-extensions. As a byproduct we obtain new rigidity results in C∗-algebra theory including additional examples of C∗-superrigid groups and explicit computations of symmetries of reduced group C∗-algebras.
Mathematics - Group Theory Mathematics - Operator Algebras

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