$C^{\ast }$-rigidity of the Heisenberg group

Abstract

We prove that the Heisenberg groups can be distinguished from the other connected and simply connected Lie groups via their group $C^{\ast }$-algebras. The main step of the proof is a characterization of the nilpotent Lie groups among the solvable Lie groups solely in terms of topological properties of their coadjoint orbits.

13 pages, accepted for publication in Publ. RIMS