A topological invariant for continuous fields of Cuntz algebras

  title={A topological invariant for continuous fields of Cuntz algebras},
  author={T. Sogabe},
  journal={Mathematische Annalen},
  • T. Sogabe
  • Published 17 February 2020
  • Mathematics
  • Mathematische Annalen
We wish to investigate continuous fields of the Cuntz algebras. The Cuntz algebras $${\mathcal {O}}_{n+1}, n\ge 1$$ O n + 1 , n ≥ 1 play an important role in the theory of operator algebras, and they are characterized by their K-groups $$K_0({\mathcal {O}}_{n+1})={\mathbb {Z}}_n$$ K 0 ( O n + 1 ) = Z n , the cyclic groups of order $$n\ge 1$$ n ≥ 1 . Since the mod n K-group for a compact Hausdorff space can be realized by the K-group of the trivial continuous field of $${\mathcal {O}}_{n+1}$$ O… 
Equivariant higher Dixmier-Douady Theory for circle actions on UHF-algebras
We develop an equivariant Dixmier-Douady theory for locally trivial bundles of C-algebras with fibre D⊗K equipped with a fibrewise T-action, where T denotes the circle group and D = End (V ) for a
Kirchberg algebras with the same homotopy groups of their automorphism groups
We determine when two unital UCT Kirchberg algebras with finitely generated K-groups have the same homotopy groups of their automorphism groups and reveal a kind of duality between two algebras given


$${\mathcal{C}}_{0}$$ (X)-algebras, stability and strongly self-absorbing $${\mathcal{C}}^{*}$$ -algebras
We study permanence properties of the classes of stable and so-called $${\mathcal{D}}$$-stable $${\mathcal{C}}^{*}$$-algebras, respectively. More precisely, we show that a $${\mathcal{C}}_{0}$$
Suppose that A is a C*-algebra for which $A \cong A \otimes {\mathcal Z}$, where ${\mathcal Z}$ is the Jiang–Su algebra: a unital, simple, stably finite, separable, nuclear, infinite-dimensional
On the KK-theory of strongly self-absorbing C*-algebras
Let $\Dh$ and $A$ be unital and separable $C^{*}$-algebras; let $\Dh$ be strongly self-absorbing. It is known that any two unital $^*$-homomorphisms from $\Dh$ to $A \otimes \Dh$ are approximately
Fiberwise KK -equivalence of continuous fields of C*-algebras
Let A and B be separable nuclear continuous C(X)-algebras over a finite dimensional compact metrizable space X. It is shown that an element $\sigma$ of the parametrized Kasparov group KK_X(A,B) is
The C*-algebra of a vector bundle
Abstract We prove that the Cuntz–Pimsner algebra OE of a vector bundle E of rank ≧ 2 over a compact metrizable space X is determined up to an isomorphism of C(X)-algebras by the ideal (1 − [E])K0(X)
A Dixmier--Douady theory for strongly self-absorbing C*-algebras
Abstract We show that the Dixmier–Douady theory of continuous fields of C*C^{*}-algebras with compact operators 𝕂{\mathbb{K}} as fibers extends significantly to a more general theory of fields with
Poly-ℤ Group Actions on Kirchberg Algebras I
Toward the complete classification of poly-${\mathbb{Z}}$ group actions on Kirchberg algebras, we prove several fundamental theorems that are used in the classification. In addition, as an
The homotopy groups of the automorphism groups of Cuntz–Toeplitz algebras
  • T. Sogabe
  • Mathematics
    Journal of the Mathematical Society of Japan
  • 2020
The Cuntz-Toeplitz algebra $E_{n+1}$ for $n\geq1$ is the universal C*-algebra generated by $n+1$ isometries with mutually orthogonal ranges. In this paper, we investigate the automorphism groups of
Nonstable K-theory for Z-stable C*-algebras
Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state. Let A != 0 be a unital C^*-algebra with A = A tensor Z. Then the homotopy groups of the group U(A) of