کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4591181 | 1335014 | 2012 | 33 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: When is the Cuntz–Krieger algebra of a higher-rank graph approximately finite-dimensional? When is the Cuntz–Krieger algebra of a higher-rank graph approximately finite-dimensional?](/preview/png/4591181.png)
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.
Journal: Journal of Functional Analysis - Volume 263, Issue 1, 1 July 2012, Pages 183-215