Description
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.
Details
Title
- Functorial results for C*-algebras of higher-rank graphs
Contributors
- Eikenberry, Keenan (Author)
- Quigg, John (Thesis advisor)
- Kaliszewski, Steven (Thesis advisor)
- Spielberg, John (Committee member)
- Arizona State University (Publisher)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2016
Subjects
Resource Type
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Note
- thesisPartial requirement for: M.A., Arizona State University, 2016
- bibliographyIncludes bibliographical references (pages 46-47)
- Field of study: Mathematics
Citation and reuse
Statement of Responsibility
by Keenan Eikenberry