On the classification of nonsimple graph C*-algebras

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Standard

On the classification of nonsimple graph C*-algebras. / Eilers, Søren; Tomforde, Mark.

I: Mathematische Annalen, Bind 346, 2010, s. 393-418.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Eilers, S & Tomforde, M 2010, 'On the classification of nonsimple graph C*-algebras', Mathematische Annalen, bind 346, s. 393-418.

APA

Eilers, S., & Tomforde, M. (2010). On the classification of nonsimple graph C*-algebras. Mathematische Annalen, 346, 393-418.

Vancouver

Eilers S, Tomforde M. On the classification of nonsimple graph C*-algebras. Mathematische Annalen. 2010;346:393-418.

Author

Eilers, Søren ; Tomforde, Mark. / On the classification of nonsimple graph C*-algebras. I: Mathematische Annalen. 2010 ; Bind 346. s. 393-418.

Bibtex

@article{d1f69440a1fd11df928f000ea68e967b,
title = "On the classification of nonsimple graph C*-algebras",
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.",
author = "S{\o}ren Eilers and Mark Tomforde",
note = "Keywords: math.OA; 46L55",
year = "2010",
language = "English",
volume = "346",
pages = "393--418",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer",

}

RIS

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