C*-algebras of stable rank one and their Cuntz semigroups

The uncovering of new structure on the Cuntz semigroup of a C*-algebra of stable rank one leads to several applications: we answer affirmatively, for the class of stable rank-one C*-algebras, a conjecture by Blackadar and Handelman on dimension functions, the global Glimm halving problem, and the pr...

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Detalles Bibliográficos
Autores: Antoine Riolobos, Ramon|||0000-0002-0062-5938, Perera Domènech, Francesc|||0000-0002-4669-4736, Robert, Leonel, Thiel, Hannes
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:306023
Acceso en línea:https://ddd.uab.cat/record/306023
https://dx.doi.org/urn:doi:10.1215/00127094-2021-0009
Access Level:acceso abierto
Palabra clave:Cuntz semigroup
C*-algebra
Stable rank one
Hilbert C*-module
Semilattice
Descripción
Sumario:The uncovering of new structure on the Cuntz semigroup of a C*-algebra of stable rank one leads to several applications: we answer affirmatively, for the class of stable rank-one C*-algebras, a conjecture by Blackadar and Handelman on dimension functions, the global Glimm halving problem, and the problem of realizing functions on the cone of 2-quasitraces as ranks of Cuntz semigroup elements. We also gain new insights into the comparability properties of positive elements in C*-algebras of stable rank one.