3 papers
math.OA2021
The Cuntz semigroup of unital commutative AI-algebras
Eduard Vilalta
We provide an abstract characterization for the Cuntz semigroup of unital commutative AI-algebras, as well as a characterization for abstract Cuntz semigroups of the form $\text{Ls…
math.OA2021
Covering dimension of Cuntz semigroups II
Hannes Thiel, Eduard Vilalta
We show that the dimension of the Cuntz semigroup of a C*-algebra is determined by the dimensions of the Cuntz semigroups of its separable sub-C*-algebras. This allows us to remove…
math.OA2021
A local characterization for the Cuntz semigroup of AI-algebras
Eduard Vilalta
We give a local characterization for the Cuntz semigroup of AI-algebras building upon Shen's characterization of dimension groups. Using this result, we provide an abstract charact…