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Obstructions to 𝒵-Stability for Unital Simple C*-Algebras

Published online by Cambridge University Press:  20 November 2018

Guihua Gong ,
Xinhui Jiang  and
Hongbing Su
Guihua Gong
Affiliation:
Mathematics Department, University of Puerto Rico, P.O. Box 23355, San Juan, Puerto Rico 00931, email: ggong@rrpac.upr.clu.edu
Xinhui Jiang
Affiliation:
The Fields Institute, 222 College Street, Toronto, Ontario M5T 3J1, email: jiang@fields.utoronto.ca
Hongbing Su
Affiliation:
The Fields Institute, 222 College Street, Toronto, Ontario M5T 3J1, email: su@fields.utoronto.ca
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Abstract

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Let $\text{Z}$ be the unital simple nuclear infinite dimensional ${{C}^{*}}$-algebra which has the same Elliott invariant as $\mathbb{C}$, introduced in [9]. A ${{C}^{*}}$-algebra is called $\text{Z}$-stable if $A\,\cong \,A\,\otimes \,\text{Z}$. In this note we give some necessary conditions for a unital simple ${{C}^{*}}$-algebra to be $\text{Z}$-stable.

Keywords

46L05simple C*-algebra𝒵-stabilityweak (un)perforation in K0 groupproperty Γfiniteness.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 4 , 01 December 2000 , pp. 418 - 426
Copyright
Copyright © Canadian Mathematical Society 2000

References

[1] Blackadar, B., K-Theory for Operator Algebras.Math. Sci. Res. Inst. Publ. 5, Springer-Verlag, New York, 1986.Google Scholar
[2] Blackadar, B., Rational C*-algebras and nonstable K-theory. Rocky MountainMath. J. 20 (1990), 285–316.Google Scholar
[3] Blackadar, B. and Kumjian, A., Skew product of relations and the structure of simple C*-algebras. Math. Z. 189 (1985), 55–63.Google Scholar
[4] Blackadar, B., Kumjian, A. and Rordam, M., Approximately central matrix units and the structure of noncommutative tori. K-theory 6 (1992), 267–284.Google Scholar
[5] Connes, A., Outer conjugacy classes of automorphisms of factors. Ann. Sci. Ecole Norm. Sup. 8 (1975), 383–419.Google Scholar
[6] Cuntz, J., The structure of addition and multiplication in simple C*-algebras. Math. Scand. 40 (1977), 215–233.Google Scholar
[7] Cuntz, J., K-theory for certain C*-algebras. Ann.Math. 113 (1981), 181–197.Google Scholar
[8] Elliott, G. A., The classification problem for amenable C*-algebras. Proceedings ICM ‘94, 922–932.Google Scholar
[9] Jiang, X. and Su, H., On a simple unital projectionless C*-algebra. Amer. J. Math., to appear.Google Scholar
[10] Lin, H. and Phillips, N. C., Classification of direct limits of even Cuntz-circle algebras. Mem. Amer.Math. Soc. (565) 118, 1995.Google Scholar
[11] McDuff, D., Central sequences and the hyperfinite factor. Proc. LondonMath. Soc. 21 (1970), 443–461.Google Scholar
[12] Murray, F. J. and von Neumann, J., On rings of operators, IV. Ann. of Math. (2) 44 (1943), 716–808.Google Scholar
[13] Rordam, M., On the structure of simple C*-algebras tensored with a UHF-algebra I. J. Funct. Anal. 100 (1991), 1–17.Google Scholar
[14] Villadsen, J., Simple C*-algebras with perforation. Preprint.Google Scholar