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

By Ramon Antoine, F. Perera, Leonel Robert, Hannes Thiel. Duke mathematical journal, 2018

66 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/409ec2eaa314ac02702b7f77f088bcbdf85a9af8