New examples of W^* and C^*-superrigid groups

2020/10/02 by Ionuţ Chifan, Chifan, Ionut, Alec Diaz-Arias +3 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2010.01223

openalex publication_date 2020/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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