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Classification theorems for the C*-Algebras of graphs with sinks

Published online by Cambridge University Press:  17 April 2009

Iain Raeburn ,
Mark Tomforde  and
Dana P. Williams
Iain Raeburn
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia, e-mail: iain@math.newcastle.edu.au
Mark Tomforde
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States of America, e-mail: tomforde@math.uiowa.edu
Dana P. Williams
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, NH 03755, United States of America e-mail: dana.williams@dartmouth.edu
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We consider graphs E which have been obtained by adding one or more sinks to a fixed directed graph G. We classify the C*-algebra of E up to a very strong equivalence relation, which insists, loosely speaking, that C*(G) is kept fixed. The main invariants are vectors WE: G0 → ℕ which describe how the sinks are attached to G; more precisely, the invariants are the classes of the WE in the cokernel of the map A – I, where A is the adjacency matrix of the graph G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 1 , August 2004 , pp. 143 - 161
Copyright
Copyright © Australian Mathematical Society 2004

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