The connected stable rank of the purely infinite simple $C^*$-algebras
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- by Yifeng Xue PDF
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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 $\operatorname {csr}(\mathcal A)=2$.References
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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
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 3671-3676
- MSC (1991): Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-99-05397-6
- MathSciNet review: 1670439