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Tracially Quasidiagonal Extensions

Published online by Cambridge University Press:  20 November 2018

Huaxin Lin
Huaxin Lin*
Affiliation:
Department of Mathematics East China Normal University Shanghai China
*
Current address: Department of Mathematics University of Oregon Eugene, Oregon 97403-1222 USA
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Abstract

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It is known that a unital simple ${{C}^{*}}$-algebra $A$ with tracial topological rank zero has real rank zero. We show in this note that, in general, there are unital ${{C}^{*}}$-algebras with tracial topological rank zero that have real rank other than zero.

Let $0\,\to \,J\,\to \,E\,\to A\,\to \,0$ be a short exact sequence of ${{C}^{*}}$-algebras. Suppose that $J$ and $A$ have tracial topological rank zero. It is known that $E$ has tracial topological rank zero as a ${{C}^{*}}$-algebra if and only if $E$ is tracially quasidiagonal as an extension. We present an example of a tracially quasidiagonal extension which is not quasidiagonal.

Keywords

46L0546L80tracially quasidiagonal extensionstracial rank
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 3 , 01 September 2003 , pp. 388 - 399
Copyright
Copyright © Canadian Mathematical Society 2003

Footnotes

Research partially supported by NSF grant DMS 0097903.

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