On the classification of nonsimple graph C*-algebras

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

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

I: Mathematische Annalen, Bind 346, Nr. 2, 01.11.2009, s. 393-418.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Eilers, S & Tomforde, M 2009, 'On the classification of nonsimple graph C*-algebras', Mathematische Annalen, bind 346, nr. 2, s. 393-418. https://doi.org/10.1007/s00208-009-0403-z

APA

Eilers, S., & Tomforde, M. (2009). On the classification of nonsimple graph C*-algebras. Mathematische Annalen, 346(2), 393-418. https://doi.org/10.1007/s00208-009-0403-z

Vancouver

Eilers S, Tomforde M. On the classification of nonsimple graph C*-algebras. Mathematische Annalen. 2009 nov. 1;346(2):393-418. https://doi.org/10.1007/s00208-009-0403-z

Author

Eilers, Søren ; Tomforde, Mark. / On the classification of nonsimple graph C*-algebras. I: Mathematische Annalen. 2009 ; Bind 346, Nr. 2. s. 393-418.

Bibtex

@article{340886e5b3094d6593961c2c9da1ae66,
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",
year = "2009",
month = nov,
day = "1",
doi = "10.1007/s00208-009-0403-z",
language = "English",
volume = "346",
pages = "393--418",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer",
number = "2",

}

RIS

TY - JOUR

T1 - On the classification of nonsimple graph C*-algebras

AU - Eilers, Søren

AU - Tomforde, Mark

PY - 2009/11/1

Y1 - 2009/11/1

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.

UR - http://www.scopus.com/inward/record.url?scp=76149127332&partnerID=8YFLogxK

U2 - 10.1007/s00208-009-0403-z

DO - 10.1007/s00208-009-0403-z

M3 - Journal article

AN - SCOPUS:76149127332

VL - 346

SP - 393

EP - 418

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 2

ER -

ID: 233961211