Geometric & Functional Analysis GAFA

, Volume 15, Issue 2, pp 377–415 | Cite as

Purely infinite C*-Algebras: Ideal-preserving zero homotopies

Original Paper

Abstract.

We show that if A is a separable, nuclear, \(\mathcal{O}_\infty \)-absorbing (or strongly purely infinite) C*-algebra which is homotopic to zero in an ideal-system preserving way, then A is the inductive limit of C*-algebras of the form \(C_0 (\Gamma ,\upsilon ) \otimes M_k ,\) where Γ is a finite connected graph (and \(C_0 (\Gamma ,\upsilon )\) is the algebra of continuous functions on Γ that vanish at a distinguished point \(\upsilon \in \Gamma \)).

We show further that if B is any separable, nuclear C*-algebra, then \(B \otimes \mathcal{O}_2 \otimes \mathcal{K}\) is isomorphic to a crossed product \(D \rtimes_{\alpha} \mathbb{Z},\) where D is an inductive limit of C*-algebras of the form \(C_0 (\Gamma ,\upsilon ) \otimes M_k \) (and D is \(\mathcal{O}_2 \) -absorbing and homotopic to zero in an ideal-system preserving way).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Department of MathematicsUniversity of Southern DenmarkOdense MDenmark

Personalised recommendations