abstract: Higher-rank graphs, or k-graphs, are higher-dimensional analogues of directed graphs, and as with ordinary directed graphs, there are various C*-algebraic objects that can be associated with them. This thesis adopts a functorial approach to study the relationship between k-graphs and their associated C*-algebras. In particular, two functors are given between appropriate categories of higher-rank graphs and the category of C*-algebras, one for Toeplitz algebras and one for Cuntz-Krieger algebras. Additionally, the Cayley graphs of finitely generated groups are used to define a class of k-graphs, and a functor is then given from a category of finitely generated groups to the category of C*-algebras. Finally, functoriality is investigated for product systems of C*-correspondences associated to k-graphs. Additional results concerning the structural consequences of functoriality, properties of the functors, and combinatorial aspects of k-graphs are also included throughout. / Dissertation/Thesis / Masters Thesis Mathematics 2016
| Identifer | oai:union.ndltd.org:asu.edu/item:40804 |
| Date | January 2016 |
| Contributors | Eikenberry, Keenan (Author), Quigg, John (Advisor), Kaliszewski, Steven (Advisor), Spielberg, John (Committee member), Arizona State University (Publisher) |
| Source Sets | Arizona State University |
| Language | English |
| Detected Language | English |
| Type | Masters Thesis |
| Format | 51 pages |
| Rights | http://rightsstatements.org/vocab/InC/1.0/, All Rights Reserved |
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