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On the classification of nonsimple graph C *-algebras

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Søren Eilers

  2. Department of Mathematics, University of Houston, Houston, TX, 77204-3008, USA

    Mark Tomforde

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  1. Søren Eilers
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  2. Mark Tomforde
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Correspondence to Mark Tomforde.

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Eilers, S., Tomforde, M. On the classification of nonsimple graph C *-algebras. Math. Ann. 346, 393–418 (2010). https://doi.org/10.1007/s00208-009-0403-z

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  • DOI: https://doi.org/10.1007/s00208-009-0403-z

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