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.

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

Given a row-finite $k$-graph $\Lambda$ with no sources we investigate the $K$-theory of the higher rank graph $C^*$-algebra, $C^*(\Lambda)$. When $k=2$ we are able to give explicit formulae to calculate the $K$-groups of ...

Given a row-finite k-graph ? with no sources we investigate the K-theory of the higher rank graph C*-algebra, C*(?). When k=2 we are able to give explicit formulae to calculate the K-groups of C*(?). The K-groups of C*(?) ...

Cyfieithiad yw'r llyfr hwn o Linear Algebra - An Introduction a ymddangosodd gyntaf yn 1978 ac a gyhoeddwyd gan y cwmni Van Nostrand Reinhold. Cafwyd Ail Argraffiad yn 1982 a dros y blynyddoedd bu nifer o ail brintiadau. ...