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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…
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…
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…
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…
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…
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…
The Reciprocal Kirchberg Algebras
Taro Sogabe
For two unital Kirchberg algebras with finitely generated K-groups, we introduce a property, called reciprocality, which is proved to be closely related to the homotopy theory of K…
A topological invariant for continuous fields of Cuntz algebras II
Sogabe Taro
We investigate an invariant for continuous fields of the Cuntz algebra introduced in our previous work, and find a way to obtain a continuous field of $\mathbb{…
A topological invariant for continuous fields of the Cuntz algebras
Taro Sogabe
For a continuous field of the Cuntz algebra over a finite CW complex, we introduce a topological invariant, which is an element in Dadarlat-Pennig's generalized cohomology group, a…
The homotopy groups of the automorphism groups of Cuntz-Toeplitz algebras
Taro Sogabe
The Cuntz-Toeplitz algebra for is the universal C*-algebra generated by isometries with mutually orthogonal ranges. In this paper, we investigate the autom…
The group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra
Masaki Izumi, Taro Sogabe
We determine the group structure of the homotopy set whose target is the automorphism group of the Cuntz algebra for finite n in terms of K-theory. We show that there is…