Ext classes and embeddings for C*-algebras of graphs with sinks

Details Ext classes and embeddings for C*-algebras of graphs with sinks Ext classes and embeddings for C*-algebras of graphs with sinks

2001-03-08

arxiv.org/abs/math/0103056v2

New York J. Math. 7 (2001), 233--256

Mathematics

Operator Algebras

24 pages, uses XY-pic, New version comments: small typos fixed, to appear in New York J. Math

Scientific paper

We consider directed graphs E which have been obtained by adding a sink to a fixed graph G. We associate an element of Ext(C*(G)) to each such E, and show that the classes of two such graphs are equal in Ext(C*(G)) if and only if the associated C*-algebra of one can be embedded as a full corner in the C*-algebra of the other in a particular way. If every loop in G has an exit, then we are able to use this result to generalize some of the classification theorems of Raeburn, Tomforde, and Williams for C*-algebras of graphs with sinks.

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