Work

Spanier–Whitehead K-Duality and Duality of Extensions of C*-Algebras

Year: 2024

Type: article

Abstract: KK-theory is a bivariant and homotopy-invariant functor on $C^{*}$-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 $C^{*}$-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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnae242

Authors: Ulrich Pennig, Taro Sogabe

Institutions: Cardiff University, Kyoto University

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,534

Funders: Japan Society for the Promotion of Science, Research Institute for Mathematical Sciences, Division of Mathematical Sciences