Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T16:13:05.948Z Has data issue: false hasContentIssue false
  • English
  • Français

AF-Skeletons and Real Rank Zero Algebras with the Corona Factorization Property

Published online by Cambridge University Press:  20 November 2018

D. Kucerovsky  and
P. W. Ng
D. Kucerovsky
Affiliation:
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3 e-mail: [email protected]
P. W. Ng
Affiliation:
Department of Mathematics, 217 M.D. Doucet Hall, University of Louisiana at Lafayette, Lafayette, LA 70504, U.S.A. e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let $A$ be a stable, separable, real rank zero ${{C}^{*}}$-algebra, and suppose that $A$ has an AF-skeleton with only finitely many extreme traces. Then the corona algebra $\mathcal{M}\left( A \right)/A$ is purely infinite in the sense of Kirchberg and Rørdam, which implies that $A$ has the corona factorization property.

Keywords

46L8046L8519K35
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 2 , 01 June 2007 , pp. 227 - 233
Copyright
Copyright © Canadian Mathematical Society 2007

References

[1] Combes, F. and Zettl, H., Order structures, traces and weights on Morita equivalent C*-algebras. Math. Ann. 265(1983), no. 1, 67–81.Google Scholar
[2] Connes, A. and Higson, N., Déformations, morphismes asymptotiques et K-thèorie bivariante. C. R. Acad. Sci. Paris Sèr. I Math. 311(1990), no. 2, 101–106.Google Scholar
[3] Elliott, G. A. and Handelman, D. E., Addition of C*-algebra extensions. Pacific J. Math. 137(1989), no. 1, 87–121.Google Scholar
[4] Goodearl, K. R., K 0 of multiplier algebras of C*-algebras with real rank zero K-theory. 10(1996), no. 5, 419–489.Google Scholar
[5] Goodearl, K. R., Partially ordered abelian groups with interpolation. Mathematical Surveys and Monographs 20, American Mathematical Society, RI, 1986.Google Scholar
[6] Kasparov, G. G., The operator K-functor and extensions of C*-algebras. Math. USSR Izvestia 16(1981), 513–572.Google Scholar
[7] Kirchberg, E. and Rørdam, M., Nonsimple purely infinite C*-algebras. http://www.math.ku.dk/_rordam/manus/pi1.ps.gz. Google Scholar
[8] Kucerovsky, D., Large Fredholm Triples. J. Funct. Anal. 236(2006), no. 2, 395–408.Google Scholar
[9] Lin, H., Skeleton C*-algebras. Canad. J. Math. 44(1992), no. 2, 324–341.Google Scholar
[10] Perera, F. and Rørdam, M., AF-embeddings into C*-algebras of real rank zero. J. Funct. Anal. 217(2004), 142–170.Google Scholar
[11] Rørdam, M., A simple C*-algebra with a finite and an infinite projection. Acta Math. 191(2003), no. 2, 109–142.Google Scholar
[12] Zhang, S., On the structure of projections and ideals of corona algebras. Canad. J. Math. 41(1989), 721–742.Google Scholar