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math.OA2024
Total extension groups for unital Kirchberg algebras
Kengo Matsumoto, Taro Sogabe
We introduce a hierarchy for unital Kirchberg algebras with finitely generated K-groups by which the first and second homotopy groups of the automorphism groups serve as a complete…
math.OA2024
On the homotopy groups of the automorphism groups of Cuntz-Krieger algebras
Kengo Matsumoto, Taro Sogabe
In this paper, we first present the homotopy groups of the automorphism groups of Cuntz--Krieger algebras in terms of the underlying matrices of the Cuntz--Krieger algebras. We als…
math.OA2024
Spanier-Whitehead K-Duality and Duality of Extensions of -algebras
Ulrich Pennig, Taro Sogabe
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-Wh…