Pennig, Ulrich ORCID: https://orcid.org/0000-0001-5441-6130 and Sogabe, Taro 2024. Spanier–Whitehead K-duality and duality of extensions of C*-algebras. International Mathematics Research Notices 10.1093/imrn/rnae242 |
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Abstract
KK-theory is a bivariant and homotopy-invariant functor on -algebras that combines K-theory and K-homology. KK-groups form the morphisms in a triangulated category. Spanier–Whitehead K-duality intertwines the homological with the cohomological side of KK-theory. Any extension of a unital -algebra by the compacts has two natural exact triangles associated to it (the extension sequence itself and a mapping cone sequence). We find a duality (based on Spanier–Whitehead K-duality) that interchanges the roles of these two triangles together with their six-term exact sequences. This allows us to give a categorical picture for the duality of Cuntz–Krieger–Toeplitz extensions discovered by K. Matsumoto.
Item Type: | Article |
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Date Type: | Published Online |
Status: | In Press |
Schools: | Mathematics |
Publisher: | Oxford University Press |
ISSN: | 1073-7928 |
Date of First Compliant Deposit: | 25 October 2024 |
Date of Acceptance: | 3 October 2024 |
Last Modified: | 28 Oct 2024 15:00 |
URI: | https://orca.cardiff.ac.uk/id/eprint/173330 |
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