$C^*$-rigidity of the Heisenberg group
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913523081150464 |
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| author | Beltita, Ingrid Beltita, Daniel |
| author_facet | Beltita, Ingrid Beltita, Daniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09937 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $C^*$-rigidity of the Heisenberg group Beltita, Ingrid Beltita, Daniel Operator Algebras Representation Theory Primary 22E27, Secondary 22D25, 22E25, 17B30 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. |
| title | $C^*$-rigidity of the Heisenberg group |
| topic | Operator Algebras Representation Theory Primary 22E27, Secondary 22D25, 22E25, 17B30 |
| url | https://arxiv.org/abs/2407.09937 |