Abstract bivariant Cuntz semigroups
We show that abstract Cuntz semigroups form a closed symmetric monoidal category. Thus, given Cuntz semigroups S and T, there is another Cuntz semigroup [S,T] playing the role of morphisms from S to T. Applied to C∗-algebras A and B, the semigroup [Cu(A), Cu(B)] should be considered as the target in...
| 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:306046 |
| Acceso en línea: | https://ddd.uab.cat/record/306046 https://dx.doi.org/urn:doi:10.1093/imrn/rny143 |
| Access Level: | acceso abierto |
| Palabra clave: | Cuntz semigroup Tensor product Continuous poset C∗-algebra |
| Sumario: | We show that abstract Cuntz semigroups form a closed symmetric monoidal category. Thus, given Cuntz semigroups S and T, there is another Cuntz semigroup [S,T] playing the role of morphisms from S to T. Applied to C∗-algebras A and B, the semigroup [Cu(A), Cu(B)] should be considered as the target in analogues of the UCT for bivariant theories of Cuntz semigroups. Abstract bivariant Cuntz semigroups are computable in a number of interesting cases. We also show that order-zero maps between C∗-algebras naturally define elements in the respective bivariant Cuntz semigroup. |
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