New examples of W⁎ and C⁎-superrigid groups

Abstract

A countable discrete 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 Cr⁎(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.