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.

Keywords: Graph algebras, extension, semiprojectivity

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