C*-superrigidity of 2-step nilpotent groups

TL;DR

This paper proves that torsion-free finitely generated 2-step nilpotent groups are uniquely determined by their group C*-algebras, recovering their algebraic structure and nilpotency class through K-theoretic methods.

Contribution

It establishes C*-superrigidity for 2-step nilpotent groups, extending previous results to a broader class of nilpotent groups using noncommutative geometry techniques.

Findings

Group C*-algebras characterize torsion-free finitely generated nilpotent groups.

Nilpotency class and subquotients are recoverable from C*-algebras.

C*-superrigidity holds for 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.