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arXiv · 1809.03984

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

Ramon Antoine·Francesc Perera·Leonel Robert·Hannes Thiel
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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.

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Ramon Antoine, Francesc Perera, Leonel Robert, Hannes Thiel. 2018-09-11. C*-algebras of stable rank one and their Cuntz semigroups. https://arxiv.org/abs/1809.03984

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