Index maps in the K-theory of graph algebras
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Index maps in the K-theory of graph algebras. / Meier Carlsen, Toke; Eilers, Søren; Tomforde, Mark.
I: Journal of K-Theory, Bind 9, Nr. 2, 2012, s. 385-406.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Index maps in the K-theory of graph algebras
AU - Meier Carlsen, Toke
AU - Eilers, Søren
AU - Tomforde, Mark
PY - 2012
Y1 - 2012
N2 - 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 extensionin 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.
AB - 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 extensionin 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.
U2 - 10.1017/is011004017jkt156
DO - 10.1017/is011004017jkt156
M3 - Journal article
VL - 9
SP - 385
EP - 406
JO - Journal of K-Theory
JF - Journal of K-Theory
SN - 1865-2433
IS - 2
ER -
ID: 49597567