8 papers
Homotopy of inner automorphism groups of Cuntz algebras
Taro Sogabe
We show that the inner automorphism groups and automorphism groups of the Cuntz algebras have the same homotopy groups. In particular, the homotopy types of the inner automorphism…
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…
Topological full groups arising from Cuntz and Cuntz-Toeplitz algebras and their crossed products
Ryoya Arimoto, Taro Sogabe
In this paper, we investigate the topological full groups arising from the Cuntz and Cuntz-Toeplitz algebras and their crossed products with the Cartan subalgebras of Cuntz and Cun…
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…
Reciprocal Cuntz--Krieger algebras
Kengo Matsumoto, Taro Sogabe
Reciprocality in Kirchberg algebras is a duality between strong extension groups and K-theory groups. We describe a construction of the reciprocal dual algebra $\widehat{\mathcal{A…