^{1} Department of Mathematical Sciences, Faculty of Science, Københavns Universitet^{2} Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway^{3} Department of Mathematics, University of Houston, USA^{4} Department of Mathematical Sciences, Faculty of Science, Københavns Universitet

DOI:

10.1017/is011004017jkt156

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.

Type:

Journal article

Language:

English

Published in:

Journal of K-theory, 2012, Vol 9, Issue 2, p. 385-406