Covering dimension of Cuntz semigroups II
| Autor: | Hannes Thiel, Eduard Vilalta |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Mathematics::Operator Algebras Semigroup General Mathematics 010102 general mathematics Mathematics - Operator Algebras 01 natural sciences Separable space Primary 46L05 46L85 Secondary 54F45 55M10 Dimension (vector space) Mathematics::K-Theory and Homology 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Operator Algebras (math.OA) Mathematics |
| Zdroj: | International Journal of Mathematics. 32 |
| ISSN: | 1793-6519 0129-167X |
| DOI: | 10.1142/s0129167x21501007 |
| Popis: | 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 separability assumptions from previous results on the dimension of Cuntz semigroups. To obtain these results, we introduce a notion of approximation for abstract Cuntz semigroups that is compatible with the approximation of a C*-algebra by sub-C*-algebras. We show that many properties for Cuntz semigroups are preserved by approximation and satisfy a L\"owenheim-Skolem condition. Comment: 21 pages |
| Databáze: | OpenAIRE |
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