Computing Ext for graph algebras

Details Computing Ext for graph algebras Computing Ext for graph algebras

2001-03-08

arxiv.org/abs/math/0103055v3

J. Operator Theory 49 (2003), 363--387

Mathematics

Operator Algebras

23 pages, uses XY-pic, to appear in the Journal of Operator Theory, some small typos corrected

Scientific paper

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 vertex 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 which 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 transitive graph with no sinks whose associated C*-algebra is not semiprojective.

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