C*-superrigidity of 2-step nilpotent groups

Abstract

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.

16 pages; v3: accepted for publication in Adv. Math, corrected some inaccuracies, updated address and references; v2: proof of Theorem 2.2. changed, corrected error in Proposition 2.14, references added, acknowledgements added