Index maps in the K-theory of graph algebras

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Standard

Index maps in the K-theory of graph algebras. / Meier Carlsen, Toke; Eilers, Søren; Tomforde, Mark.

I: Journal of K-Theory, Bind 9, Nr. 2, 2012, s. 385-406.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Meier Carlsen, T, Eilers, S & Tomforde, M 2012, 'Index maps in the K-theory of graph algebras', Journal of K-Theory, bind 9, nr. 2, s. 385-406. https://doi.org/10.1017/is011004017jkt156

APA

Meier Carlsen, T., Eilers, S., & Tomforde, M. (2012). Index maps in the K-theory of graph algebras. Journal of K-Theory, 9(2), 385-406. https://doi.org/10.1017/is011004017jkt156

Vancouver

Meier Carlsen T, Eilers S, Tomforde M. Index maps in the K-theory of graph algebras. Journal of K-Theory. 2012;9(2):385-406. https://doi.org/10.1017/is011004017jkt156

Author

Meier Carlsen, Toke ; Eilers, Søren ; Tomforde, Mark. / Index maps in the K-theory of graph algebras. I: Journal of K-Theory. 2012 ; Bind 9, Nr. 2. s. 385-406.

Bibtex

@article{9c8dea4a494847ffb7148f6e0a311c9e,
title = "Index maps in the K-theory of graph algebras",
abstract = "Let C*(E) be the graph C*-algebra associated to a graph E and let J be a gauge-invariant ideal in C*(E). We compute the cyclic six-term exact sequence in K-theory associated to the extensionin terms of the adjacency matrix associated to E. The ordered six-term exact sequence is a complete stable isomorphism invariant for several classes of graph C*-algebras, for instance those containing a unique proper nontrivial ideal. Further, in many other cases, finite collections of such sequences constitute complete invariants.Our results allow for explicit computation of the invariant, giving an exact sequence in terms of kernels and cokernels of matrices determined by the vertex matrix of E.",
author = "{Meier Carlsen}, Toke and S{\o}ren Eilers and Mark Tomforde",
year = "2012",
doi = "10.1017/is011004017jkt156",
language = "English",
volume = "9",
pages = "385--406",
journal = "Journal of K-Theory",
issn = "1865-2433",
publisher = "Cambridge University Press",
number = "2",

}

RIS

TY - JOUR

T1 - Index maps in the K-theory of graph algebras

AU - Meier Carlsen, Toke

AU - Eilers, Søren

AU - Tomforde, Mark

PY - 2012

Y1 - 2012

N2 - Let C*(E) be the graph C*-algebra associated to a graph E and let J be a gauge-invariant ideal in C*(E). We compute the cyclic six-term exact sequence in K-theory associated to the extensionin terms of the adjacency matrix associated to E. The ordered six-term exact sequence is a complete stable isomorphism invariant for several classes of graph C*-algebras, for instance those containing a unique proper nontrivial ideal. Further, in many other cases, finite collections of such sequences constitute complete invariants.Our results allow for explicit computation of the invariant, giving an exact sequence in terms of kernels and cokernels of matrices determined by the vertex matrix of E.

AB - Let C*(E) be the graph C*-algebra associated to a graph E and let J be a gauge-invariant ideal in C*(E). We compute the cyclic six-term exact sequence in K-theory associated to the extensionin terms of the adjacency matrix associated to E. The ordered six-term exact sequence is a complete stable isomorphism invariant for several classes of graph C*-algebras, for instance those containing a unique proper nontrivial ideal. Further, in many other cases, finite collections of such sequences constitute complete invariants.Our results allow for explicit computation of the invariant, giving an exact sequence in terms of kernels and cokernels of matrices determined by the vertex matrix of E.

U2 - 10.1017/is011004017jkt156

DO - 10.1017/is011004017jkt156

M3 - Journal article

VL - 9

SP - 385

EP - 406

JO - Journal of K-Theory

JF - Journal of K-Theory

SN - 1865-2433

IS - 2

ER -

ID: 49597567