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dc.contributor.author Evans, Dafydd Gwion
dc.contributor.author Sims, Aidan
dc.date.accessioned 2012-01-18T09:23:37Z
dc.date.available 2012-01-18T09:23:37Z
dc.date.issued 2012-07-01
dc.identifier.citation Evans , D G & Sims , A 2012 , ' When is the Cuntz-Krieger algebra of a higher-rank graph approximately finite-dimensional? ' Journal of Functional Analysis , vol 263 , no. 1 , pp. 183-215 . , 10.1016/j.jfa.2012.03.024 en
dc.identifier.issn 0022-1236
dc.identifier.other PURE: 174908
dc.identifier.other dspace: 2160/7744
dc.identifier.uri http://hdl.handle.net/2160/7744
dc.description Evans, D.G and Sims, A; When is the Cuntz-Krieger algebra of a higher-rank graph approximately finite-dimensional?, preprint, arXiv:1112.4549v1 en
dc.description.abstract We investigate the question: when is a higher-rank graph C*-algebra approximately finite dimensional? We prove that the absence of an appropriate higher-rank analogue of a cycle is necessary. We show that it is not in general sufficient, but that it is sufficient for higher-rank graphs with finitely many vertices. We give a detailed description of the structure of the C*-algebra of a row-finite locally convex higher-rank graph with finitely many vertices. Our results are also sufficient to establish that if the C*-algebra of a higher-rank graph is AF, then its every ideal must be gauge-invariant. We prove that for a higher-rank graph C*-algebra to be AF it is necessary and sufficient for all the corners determined by vertex projections to be AF. We close with a number of examples which illustrate why our question is so much more difficult for higher-rank graphs than for ordinary graphs. en
dc.language.iso eng
dc.relation.ispartof Journal of Functional Analysis en
dc.subject Graph C⁎-algebra en
dc.subject C⁎-algebra en
dc.subject AF algebra en
dc.subject Higher-rank graph en
dc.subject Cuntz–Krieger algebra en
dc.title When is the Cuntz-Krieger algebra of a higher-rank graph approximately finite-dimensional? en
dc.type Text en
dc.type.publicationtype Article (Journal) en
dc.identifier.doi http://dx.doi.org/10.1016/j.jfa.2012.03.024
dc.contributor.institution Quantum Systems, Information and Control en
dc.contributor.institution Institute of Mathematics & Physics (ADT) en
dc.description.status Peer reviewed en


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