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

TL;DR

This paper investigates superrigidity properties of von Neumann and reduced C*-algebras associated with coinduced groups, providing classification results for these algebras across new group classes.

Contribution

It introduces a general notion of superrigidity for these algebras and classifies them for a broad class of coinduced groups, expanding understanding in operator algebra theory.

Findings

Classification of von Neumann algebras for coinduced groups

Superrigidity results for reduced C*-algebras

New classes of groups with algebraic rigidity properties

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.