Index maps in the K-theory of graph algebras
2011 ◽
Vol 9
(2)
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pp. 385-406
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Keyword(s):
K Theory
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AbstractLet 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.
1973 ◽
Vol 16
(4)
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pp. 517-520
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1969 ◽
Vol 21
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pp. 684-701
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Keyword(s):
1987 ◽
Vol 29
(1)
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pp. 13-19
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Keyword(s):
1961 ◽
Vol 57
(3)
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pp. 489-502
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Keyword(s):
2015 ◽
Vol 37
(2)
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pp. 337-368
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Keyword(s):
1954 ◽
Vol 2
(2)
◽
pp. 66-76
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Keyword(s):