August 22, 2025Publications of the Research Institute for Mathematical SciencesOpen Access

C*-Rigidity of the Heisenberg Group

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C*-algebras of Heisenberg groups differentiate them from other connected Lie groups, showcasing unique topological traits.
The method explores characterizations of nilpotent lie groups against solvable lie groups based on coadjoint orbits.
This analysis addresses the topology of coadjoint orbits, providing insight into the classification of nilpotent groups.
Potential broader implications for understanding group structures in mathematical analysis and topology arise from these findings.

Implication

Analysis reveals C*-algebras distinguish Heisenberg groups from other Lie groups, suggesting unique properties of nilpotent structures.

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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Cite This Study

Beltiţă et al. (2025) studied this question.

synapsesocial.com/papers/68af5231ad7bf08b1eada596 https://doi.org/10.4171/prims/61-3-6

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Implication

Analysis reveals C*-algebras distinguish Heisenberg groups from other Lie groups, suggesting unique properties of nilpotent structures.

C*-Rigidity of the Heisenberg Group

Key Points

Implication

Abstract

Discussion

Cite This Study

C*-Rigidity of the Heisenberg Group

Key Points

Implication

Abstract

Discussion

Cite This Study

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