CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Tracially Quasidiagonal Extensions

  Published:2003-09-01
 Printed: Sep 2003
  • Huaxin Lin
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

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: tracially quasidiagonal extensions, tracial rank tracially quasidiagonal extensions, tracial rank
MSC Classifications: 46L05, 46L80 show english descriptions General theory of $C^*$-algebras
$K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
46L05 - General theory of $C^*$-algebras
46L80 - $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/