On the classification of nonsimple graph C*-algebras

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

SN - 0025-5831

VL - 346

SP - 393

EP - 418

JO - Mathematische Annalen

JF - Mathematische Annalen

ER -