A local characterization for the Cuntz semigroup of AI-algebras

2021/02/26 by Vilalta, Eduard
#06F05 #19K99 #46L80 #46L85 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L05 #Secondary 06A06

paper · doi:10.48550/arxiv.2102.13557

Abstract

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 characterization for the Cuntz semigroup of AI-algebras.

Related

• The Cuntz semigroup of unital commutative AI-algebras
• Covering dimension of Cuntz semigroups
• Covering dimension of Cuntz semigroups II
• The Cuntz semigroup, a Riesz type interpolation property, comparison and the ideal property
• The Cuntz semigroup as an invariant for C*-algebras