5 papers
A class of Exel--Laca algebras reciprocal to Cuntz--Krieger algebras
Kengo Matsumoto, Taro Sogabe
The reciprocality means a duality in Kirchberg algebras between K-theory groups and strong extension groups. In the paper, we will find a certain class of unital simple Exel--Laca…
On universal property of reciprocal Kirchberg algebras and uniquely ergodic automorphisms
Kengo Matsumoto, Taro Sogabe
Reciprocality in Kirchberg algebras with finitely generated K-groups is regarded as a K-theoretic duality through K-groups and strong extension groups. We will prove that the recip…
Ergodic automorphisms on Kirchberg algebras
Kengo Matsumoto, Taro Sogabe
Combining the theory of extensions of C*-algebras and the Pimsner construction, we show that every countable infinite discrete group admits an ergodic action on arbitrary unital Ki…
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…
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…