Pullbacks, C(X)-algebras, and their Cuntz semigroup

2011/01/25 by Ramon Antoine, Antoine, Ramon, Francesc Perera +3 · 3 citations
Mathematics · #46L05 #46L35 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1101.4776

openalex publication_date 2011/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we analyse the structure of the Cuntz semigroup of certain C(X)-algebras, for compact spaces of low dimension, that have no K₁-obstruction in their fibres in a strong sense. The techniques developed yield computations of the Cuntz semigroup of some surjective pullbacks of C^*-algebras. As a consequence, this allows us to give a complete description, in terms of semigroup valued lower semicontinuous functions, of the Cuntz semigroup of C(X,A), where A is a not necessarily simple C^*-algebra of stable rank one and vanishing K₁ for each closed, two sided ideal. We apply our results to study a variety of examples.

Cited by

• Extensions of pure C*-algebras
• C^*-diagonal of inductive limit of 1-dimensional NCCW complexes
• Self-adjoint operators in Z-stable C^*-algebras with prescribed spectral data

Related

• The Cuntz semigroup of continuous fields
• The Cuntz semigroup of some spaces of dimension at most two
• The modern theory of Cuntz semigroups of C*-algebras
• The Cuntz semigroup as an invariant for C*-algebras
• Recovering the Elliott invariant from the Cuntz semigroup