Journal of Operator Theory

Volume 49, Issue 2, Spring 2003 pp. 363-387.

Computing Ext for graph algebras

Authors: Mark Tomforde
Author institution: Department of Mathematics, Hanover, NH 03755--3551, USA; Current address: Department of Mathematics, University of Iowa, Iowa City, IA 52242--1419, USA

Summary: For a row-finite graph

$G$ with no sinks and in which every loop has an exit, we construct an isomorphism between

$\ext (C^*(G))$ and

$\coker (A-I)$ , where

$A$ is the^Mvertex matrix of

$G$ . If

$c$ is the class in

$\ext(C^*(G))$ associated to a graph obtained by attaching a sink to

$G$ , then this isomorphism maps

$c$ to the class of a vector that^M describes how the sink was added. We conclude with an application in which we use this isomorphism to produce an example of a row-finite tran sitive graph with no sinks whose associated

$C^*$ -algebra is not semipr ojective.

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