Cuntz semigroups of ultraproduct C*-algebras
We prove that the category of abstract Cuntz semigroups is bicomplete. As a consequence, the category admits products and ultraproducts. We further show that the scaled Cuntz semigroup of the (ultra)product of a family of C∗-algebras agrees with the (ultra)product of the scaled Cuntz semigroups of t...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:306045 |
| Acceso en línea: | https://ddd.uab.cat/record/306045 https://dx.doi.org/urn:doi:10.1112/jlms.12343 |
| Access Level: | acceso abierto |
| Palabra clave: | Cuntz semigroup Continuous poset C∗-algebra Ultraproducts |
| Sumario: | We prove that the category of abstract Cuntz semigroups is bicomplete. As a consequence, the category admits products and ultraproducts. We further show that the scaled Cuntz semigroup of the (ultra)product of a family of C∗-algebras agrees with the (ultra)product of the scaled Cuntz semigroups of the involved C∗-algebras. As applications of our results, we compute the non-stable K-Theory of general (ultra)products of C∗-algebras and we characterize when ultraproducts are simple. We also give criteria that determine order properties of these objects, such as almost unperforation. |
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