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Purely infinite C*-Algebras: Ideal-preserving zero homotopies
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kirchberg, Eberhard Rørdam, Mikael |
| Copyright Year | 2003 |
| Abstract | 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). |
| Starting Page | 377 |
| Ending Page | 415 |
| Page Count | 39 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s00039-005-0510-2 |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0312286v1.pdf |
| Alternate Webpage(s) | http://web.math.ku.dk/~rordam/manus/AH0.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/math/0312286v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s00039-005-0510-2 |
| Volume Number | 15 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
