abstract: In this thesis, I investigate the C*-algebras and related constructions that arise from combinatorial structures such as directed graphs and their generalizations. I give a complete characterization of the C*-correspondences associated to directed graphs as well as results about obstructions to a similar characterization of these objects for generalizations of directed graphs. Viewing the higher-dimensional analogues of directed graphs through the lens of product systems, I give a rigorous proof that topological k-graphs are essentially product systems over N^k of topological graphs. I introduce a "compactly aligned" condition for such product systems of graphs and show that this coincides with the similarly-named conditions for topological k-graphs and for the associated product systems over N^k of C*-correspondences. Finally I consider the constructions arising from topological dynamical systems consisting of a locally compact Hausdorff space and k commuting local homeomorphisms. I show that in this case, the associated topological k-graph correspondence is isomorphic to the product system over N^k of C*-correspondences arising from a related Exel-Larsen system. Moreover, I show that the topological k-graph C*-algebra has a crossed product structure in the sense of Larsen. / Dissertation/Thesis / Ph.D. Mathematics 2011
| Identifer | oai:union.ndltd.org:asu.edu/item:9202 |
| Date | January 2011 |
| Contributors | Patani, Nura (Author), Kaliszewski, Steven (Advisor), Quigg, John (Advisor), Bremner, Andrew (Committee member), Kawski, Matthias (Committee member), Spielberg, John (Committee member), Arizona State University (Publisher) |
| Source Sets | Arizona State University |
| Language | English |
| Detected Language | English |
| Type | Doctoral Dissertation |
| Format | 112 pages |
| Rights | http://rightsstatements.org/vocab/InC/1.0/, All Rights Reserved |
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