A bivariant theory for the Cuntz semigroup
We introduce a bivariant version of the Cuntz semigroup as equivalence classes of order zero maps generalizing the ordinary Cuntz semigroup. The theory has many features formally analogous to KK-theory including a composition product. We establish basic properties, like additivity, stability and con...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:222873 |
| Acesso em linha: | https://ddd.uab.cat/record/222873 https://dx.doi.org/urn:doi:10.1016/j.jfa.2019.05.002 |
| Access Level: | acceso abierto |
| Palavra-chave: | Cuntz semigroup Bivariant K-theory Classification of C⁎-algebras |
| Resumo: | We introduce a bivariant version of the Cuntz semigroup as equivalence classes of order zero maps generalizing the ordinary Cuntz semigroup. The theory has many features formally analogous to KK-theory including a composition product. We establish basic properties, like additivity, stability and continuity, and study categorical aspects in the setting of local C-algebras. We determine the bivariant Cuntz semigroup for numerous examples such as when the second algebra is a Kirchberg algebra, and Cuntz homology for compact Hausdorff spaces which provides a complete invariant. Moreover, we establish identities when tensoring with strongly self-absorbing C-algebras. Finally, we show how to use the bivariant Cuntz semigroup of the present work to classify unital and stably finite C-algebras. |
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