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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The connected stable rank
of the purely infinite simple $C^*$-algebras


Author: Yifeng Xue
Journal: Proc. Amer. Math. Soc. 127 (1999), 3671-3676
MSC (1991): Primary 46L05
Published electronically: July 12, 1999
MathSciNet review: 1670439
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Abstract: Suppose that $\mathcal A$ is a unital purely infinite simple $C^*$-algebra. If the class [1] of the unit 1 in $K_0(\mathcal A)$ has torsion, then $\operatorname{csr}(\mathcal A)=\infty$; if [1] is torsion-free in $K_0(\mathcal A)$, then $\operatorname{csr}(\mathcal A)=2$. If $\mathcal A$ is a non-unital purely infinite simple $C^*$-algebra, then $\operatorname{csr}(\mathcal A)=2$.


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Additional Information

Yifeng Xue
Affiliation: Institute of Fundamental Education, East China University of Science and Technology, Shanghai 200237, People’s Republic of China
Address at time of publication: Department of Mathematics, East China University of Science and Technology, Shanghai 200237, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05397-6
PII: S 0002-9939(99)05397-6
Keywords: Purely infinite simple $C^*$-algebras, connected stable rank, $K$-group of the $C^*$-algebras.
Received by editor(s): August 1, 1997
Received by editor(s) in revised form: February 24, 1998
Published electronically: July 12, 1999
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society