Lie ideals in properly infinite C*-algebras

Autor:	Thiel, Hannes
Rok vydání:	2024
Předmět:	Mathematics - Operator Algebras Mathematics - Rings and Algebras Primary 46L05 46L10. Secondary 16W10 17B60 47B47
Druh dokumentu:	Working Paper
Popis:	We show that every Lie ideal in a unital, properly infinite 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 Bre\v{s}ar, Kissin, and Shulman. Comment: 22 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.16087 Zobrazit plný text záznamu View this record from Arxiv