C*-algebras of stable rank one and their Cuntz semigroups
Ramon Antoine, Francesc Perera, Leonel Robert, Hannes Thiel
2022Dipòsit Digital de Documents de la UAB (Universitat Autònoma de Barcelona)34 citationsDOIOpen Access PDF
Abstract
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.
Topics & Concepts
MathematicsSemigroupRank (graph theory)ComparabilityConjecturePure mathematicsCone (formal languages)Dimension (graph theory)Class (philosophy)Algebra over a fieldCombinatoricsComputer scienceArtificial intelligenceAlgorithmAdvanced Operator Algebra ResearchAdvanced Banach Space TheoryAdvanced Topics in Algebra