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...

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Detalles Bibliográficos
Autores: Antoine Riolobos, Ramon|||0000-0002-0062-5938, Perera Domènech, Francesc|||0000-0002-4669-4736, Thiel, Hannes
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
Descripción
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.