Name: $C^{*}$-Rigidity of the Heisenberg Group
Keywords: Primary 22E27, Secondary 22D25, 22E25, 17B30, Mathematics - Operator Algebras, FOS: Mathematics, Representation Theory (math.RT), Operator Algebras (math.OA), Mathematics - Representation Theory

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 22 Aug 2025Embargo end date: 01 Jan 2024Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Publications of the Research Institute for Mathematical Sciences, volume 61, pages 487-502 (issn: 0034-5318, eissn: 1663-4926,

Authors: Ingrid Beltiţă; Daniel Beltiţă;

doi: 10.4171/prims/61-3-6 , 10.13140/rg.2.2.23824.42245 , 10.48550/arxiv.2407.09937

arXiv: http://arxiv.org/abs/2407.09937

$C^{*}$-Rigidity of the Heisenberg Group

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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.

Related Organizations

Romanian Academy
Romania

Keywords

Primary 22E27, Secondary 22D25, 22E25, 17B30, Mathematics - Operator Algebras, FOS: Mathematics, Representation Theory (math.RT), Operator Algebras (math.OA), Mathematics - Representation Theory

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