Strong $C^*$-rigidity of the Heisenberg groups

TL;DR

This paper establishes a strong rigidity property of Heisenberg groups, showing they can be uniquely identified among 1-connected Lie groups through their unitary duals and the Morita equivalence class of their group C*-algebras.

Contribution

The paper proves that Heisenberg groups are uniquely characterized among 1-connected Lie groups by their C*-algebra Morita equivalence class, demonstrating a form of C*-rigidity.

Findings

Heisenberg groups are distinguished by their unitary duals.

Heisenberg groups' C*-algebras are Morita invariant.

This rigidity property is strong among 1-connected Lie groups.

Abstract

We prove a strong rigidity property of the Heisenberg groups, that is, they can be distinguished from any other 1-connected Lie groups via their unitary dual spaces, in particular via the Morita equivalence class of their group $C^*$-algebras.