Spanier–Whitehead K-duality and duality of extensions of C*-algebras

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 2024 (23) , pp. 14321-14351. 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
Date Type:	Publication
Status:	Published
Schools:	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:	21 Jan 2025 14:22
URI:	https://orca.cardiff.ac.uk/id/eprint/173330

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