dc.contributor.author 
Evans, Dafydd Gwion 

dc.contributor.author 
Sims, Aidan 

dc.date.accessioned 
20120118T09:23:37Z 

dc.date.available 
20120118T09:23:37Z 

dc.date.issued 
20120701 

dc.identifier.citation 
Evans , D G & Sims , A 2012 , ' When is the CuntzKrieger algebra of a higherrank graph approximately finitedimensional? ' Journal of Functional Analysis , vol 263 , no. 1 , pp. 183215 . , 10.1016/j.jfa.2012.03.024 
en 
dc.identifier.issn 
00221236 

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 CuntzKrieger algebra of a higherrank graph approximately finitedimensional?, preprint, arXiv:1112.4549v1 
en 
dc.description.abstract 
We investigate the question: when is a higherrank graph C*algebra approximately finite dimensional? We prove that the absence of an appropriate higherrank analogue of a cycle is necessary. We show that it is not in general sufficient, but that it is sufficient for higherrank graphs with finitely many vertices. We give a detailed description of the structure of the C*algebra of a rowfinite locally convex higherrank graph with finitely many vertices. Our results are also sufficient to establish that if the C*algebra of a higherrank graph is AF, then its every ideal must be gaugeinvariant. We prove that for a higherrank 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 higherrank 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 
Higherrank graph 
en 
dc.subject 
Cuntz–Krieger algebra 
en 
dc.title 
When is the CuntzKrieger algebra of a higherrank graph approximately finitedimensional? 
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 