C⁎-superrigidity of 2-step nilpotent groups

We show that torsion-free finitely generated nilpotent groups are characterised by their group C⁎-algebras and we additionally recover their nilpotency class as well as the subquotients of the upper central series. We then use a C⁎-bundle decomposition and apply K-theoretic methods based on noncommutative tori to prove that every torsion-free finitely generated 2-step nilpotent group can be recovered from its group C⁎-algebra.