## Illinois Journal of Mathematics

### Computing $K$-theory and $\mathrm{Ext}$ for graph $C^*$-algebras

#### Abstract

$K$-theory and $\mathrm{Ext}$ are computed for the $C^*$-algebra $C^*(E)$ of any countable directed graph $E$. The results generalize the $K$-theory computations of Raeburn and Szymański and the $\mathrm{Ext}$ computations of Tomforde for row-finite graphs. As a consequence, it is shown that if $A$ is a countable $\{0,1\}$ matrix and $E_A$ is the graph obtained by viewing $A$ as a vertex matrix, then $C^*(E_A)$ is not necessarily Morita equivalent to the Exel-Laca algebra $\mathcal{O}_A$.

#### Article information

Source
Illinois J. Math., Volume 46, Number 1 (2002), 81-91.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258136141

Digital Object Identifier
doi:10.1215/ijm/1258136141

Mathematical Reviews number (MathSciNet)
MR1936076

Zentralblatt MATH identifier
1024.46023

#### Citation

Drinen, D.; Tomforde, M. Computing $K$-theory and $\mathrm{Ext}$ for graph $C^*$-algebras. Illinois J. Math. 46 (2002), no. 1, 81--91. doi:10.1215/ijm/1258136141. https://projecteuclid.org/euclid.ijm/1258136141