AF ALGEBRAS ASSOCIATED TO ORIENTED COMBINATORIAL DATA

One of the remarkable features of the construction of C*-algebras from directed graphs is the characterization of approximate finite dimensionality: the C*-algebra is AF if and only if the graph has no directed cycle. This construction has been generalized to other classes of oriented combinatorial objects, most notably the higher rank graphs. Evans and Sims investigated the question of approximate finite dimensionality in this context. On the one hand, they generalized the notion of directed cycle, and showed that a higher rank graph whose C*-algebra is AF cannot contain such a generalized cycle. They also give intriguing examples without generalized cycles that resist identification as AF algebras. In this talk, I will describe a further generalization of higher rank graphs, and will present some examples reminiscent of those of Evans and Sims, but where the AF question can be resolved. This is joint work with Ian Mitscher.