dc.contributor.author
Bosa, J.
dc.contributor.author
Tornetta, G.
dc.contributor.author
Zacharias, J.
dc.date.accessioned
2021-03-19T00:01:00Z
dc.date.accessioned
2024-09-19T14:29:01Z
dc.date.available
2021-03-19T00:01:00Z
dc.date.available
2024-09-19T14:29:01Z
dc.date.created
2019-01-01
dc.date.issued
2019-01-01
dc.identifier.uri
http://hdl.handle.net/2072/445796
dc.description.abstract
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. © 2019 The Authors
eng
dc.format.extent
37 p.
cat
dc.publisher
Academic Press Inc.
cat
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.title
A bivariant theory for the Cuntz semigroup
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/publishedVersion
cat
dc.embargo.terms
12 mesos
cat
dc.identifier.doi
10.1016/j.jfa.2019.05.002
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
