Free nilpotent groups are C*-superrigid

Abstract

The free nilpotent group Gm,n of class m and rank n is the free object on n generators in the category of nilpotent groups of class at most m. We show that Gm,n can be recovered from its reduced group C∗-algebra, in the sense that if H is any group such that C∗ r(H) is isomorphic to C∗ r(Gm,n), then H must be isomorphic to Gm,n.