## Illinois Journal of Mathematics

### The extensions of $C^*$-algebras with tracial topological rank no more than one

#### Abstract

Let $0\rightarrow I\rightarrow A\rightarrow A/I \rightarrow 0$ be a short exact sequence of $C^*$-algebras with $A$ unital. Suppose that $I$ has tracial topological rank no more than one and $A/I$ is TAI (in particular, if $A/I$ is simple and has tracial topological rank no more than one). It will be proved that $A$ has tracial topological rank no more than one if the extension is quasidiagonal, and $A$ has the property ($P_1$) if the extension is tracially quasidiagonal.

#### Article information

Source
Illinois J. Math., Volume 53, Number 2 (2009), 441-462.

Dates
First available in Project Euclid: 23 February 2010

https://projecteuclid.org/euclid.ijm/1266934787

Digital Object Identifier
doi:10.1215/ijm/1266934787

Mathematical Reviews number (MathSciNet)
MR2594638

Zentralblatt MATH identifier
1188.46031

#### Citation

Fang, Xiaochun; Zhao, Yile. The extensions of $C^*$-algebras with tracial topological rank no more than one. Illinois J. Math. 53 (2009), no. 2, 441--462. doi:10.1215/ijm/1266934787. https://projecteuclid.org/euclid.ijm/1266934787

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