A revised augmented Cuntz semigroup

2019/04/07 by Robert, Leonel, Santiago, Luis · 1 citation
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1904.03690

Abstract

We revise the construction of the augmented Cuntz semigroup functor used by the first author to classify inductive limits of 1-dimensional noncommutative CW complexes. The original construction has good functorial properties when restricted to the class of C*-algebras of stable rank one. The construction proposed here has good properties for all C*-algebras: We show that the augmented Cuntz semigroup is a stable, continuous, split exact functor, from the category of C*-algebras to the category of Cu-semigroups.

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