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arXiv · 2407.09937

$C^*$-rigidity of the Heisenberg group

Ingrid Beltita·Daniel Beltita
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Abstract

We prove that the Heisenberg groups can be distinguished from the other connected and simply connected Lie groups via their group $C^*$-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.

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Ingrid Beltita, Daniel Beltita. 2024-07-13. $C^*$-rigidity of the Heisenberg group. https://arxiv.org/abs/2407.09937

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