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Functorial Results for C*-Algebras of Higher-Rank Graphs

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

Identiferoai:union.ndltd.org:asu.edu/item:40804
Date January 2016
ContributorsEikenberry, Keenan (Author), Quigg, John (Advisor), Kaliszewski, Steven (Advisor), Spielberg, John (Committee member), Arizona State University (Publisher)
Source SetsArizona State University
LanguageEnglish
Detected LanguageEnglish
TypeMasters Thesis
Format51 pages
Rightshttp://rightsstatements.org/vocab/InC/1.0/, All Rights Reserved

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