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.
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- Partial requirement for: Ph.D., Arizona State University, 2011Note typethesis
- Includes bibliographical references (p. 100-104)Note typebibliography
- Field of study: Mathematics