$W^*$ and $C^*$-superrigidity results for coinduced groups

Abstract

In this paper we explore a generic notion of superrigidity for von Neumann algebras L(G) and reduced C * -algebras C * r (G) associated with countable discrete groups G. This allows us to classify these algebras for various new classes of groups G from the realm of coinduced groups. I.C. has been supported in part by the NSF grants DMS-1600688, FRG DMS-1854194 and a CDA award from the University of Iowa. A.D-A. was supported in part by the AGEP-supplemental grant. D.D. holds the postdoctoral fellowship fundamental research 12T5221N of the Research Foundation -Flanders.