Illinois Journal of Mathematics

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

D. Drinen and M. Tomforde

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$K$-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

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

First available in Project Euclid: 13 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
Secondary: 19K56: Index theory [See also 58J20, 58J22] 46M15: Categories, functors {For $K$-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20}


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.

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