On the classification of nonsimple graph C*-algebras
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On the classification of nonsimple graph C*-algebras. / Eilers, Søren; Tomforde, Mark.
In: Mathematische Annalen, Vol. 346, 2010, p. 393-418.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - On the classification of nonsimple graph C*-algebras
AU - Eilers, Søren
AU - Tomforde, Mark
N1 - Keywords: math.OA; 46L55
PY - 2010
Y1 - 2010
N2 - We prove that a graph C*-algebra with exactly one proper nontrivial ideal is classified up to stable isomorphism by its associated six-term exact sequence in K-theory. We prove that a similar classification also holds for a graph C*-algebra with a largest proper ideal that is an AF-algebra. Our results are based on a general method developed by the first named author with Restorff and Ruiz. As a key step in the argument, we show how to produce stability for certain full hereditary subalgebras associated to such graph C*-algebras. We further prove that, except under trivial circumstances, a unique proper nontrivial ideal in a graph C*-algebra is stable.
AB - We prove that a graph C*-algebra with exactly one proper nontrivial ideal is classified up to stable isomorphism by its associated six-term exact sequence in K-theory. We prove that a similar classification also holds for a graph C*-algebra with a largest proper ideal that is an AF-algebra. Our results are based on a general method developed by the first named author with Restorff and Ruiz. As a key step in the argument, we show how to produce stability for certain full hereditary subalgebras associated to such graph C*-algebras. We further prove that, except under trivial circumstances, a unique proper nontrivial ideal in a graph C*-algebra is stable.
M3 - Journal article
VL - 346
SP - 393
EP - 418
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
ER -
ID: 21255139