Open Collections

Description

It is a classical problem to recover a discrete group from various rings or algebras associated with it, such as the integral group ring. By analogy, in an operator algebraic framework we want to recover torsion-free groups from certain topological completions of the complex group ring, such as the reduced group $C^*$-algebra. Groups for which this is possible are called $C^*$-superrigid. My talk will discuss how a group can be recovered from its group rings, before I introduce the reduced group $C^*$-algebras and describe the state-of-the-art in $C^*$-superrigidity. I will end with a short account on other kinds of superrigidity for group operator algebras putting the subject into a bigger perspective.