Lie ideals in properly infinite C ∗ -algebras
Thiel, Hannes (Chalmers University of Technology)

Date:	2026
Abstract:	We show that every Lie ideal in a unital, properly in nite C*-algebra is commutator-equivalent to a unique two-sided ideal. It follows that the Lie ideal structure of such a C*-algebra is concisely encoded by its lattice of two-sided ideals. This answers a question of Robert in this setting. We obtain similar structure results for Lie ideals in unital, real rank zero C*-algebras without characters. As an application, we show that every Lie ideal in a von Neumann algebra is related to a unique two-sided ideal, which solves a problem of Bresar, Kissin, and Shulman.
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Lie ideals ; C*-algebras ; Properly in nite ; Von neumann algebras ; Commutators ; Square-zero elements
Published in:	Publicacions matemàtiques, Vol. 70, Num. 2 (2026) , p. 525-548 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/1500000000000146
DOI: 10.5565/PUBLMAT7022609

24 p, 1.0 MB

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