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Index maps in the K-theory of graph algebras

Published online by Cambridge University Press:  17 May 2011

Toke Meier Carlsen ,
Søren Eilers  and
Mark Tomforde
Toke Meier Carlsen
Affiliation:
Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norwaytokemeie@math.ntnu.no
Søren Eilers
Affiliation:
Department for Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmarkeilers@math.ku.dk
Mark Tomforde
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3008, USAtomforde@math.uh.edu
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Abstract

Let C*(E) be the graph C*-algebra associated to a graph E and let J be a gauge-invariant ideal in C*(E). We compute the cyclic six-term exact sequence in K-theory associated to the extension

in terms of the adjacency matrix associated to E. The ordered six-term exact sequence is a complete stable isomorphism invariant for several classes of graph C*-algebras, for instance those containing a unique proper nontrivial ideal. Further, in many other cases, finite collections of such sequences constitute complete invariants.

Our results allow for explicit computation of the invariant, giving an exact sequence in terms of kernels and cokernels of matrices determined by the vertex matrix of E.

Keywords

Graph C*-algebrasclassificationextensionsK-theory
Type
Research Article
Information
Journal of K-Theory , Volume 9 , Issue 2 , April 2012 , pp. 385 - 406
Copyright
Copyright © ISOPP 2011

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