155124-Thumbnail Image.png
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

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.
Reuse Permissions


  • Download restricted.

    Details

    Title
    • Functorial results for C*-algebras of higher-rank graphs
    Contributors
    Date Created
    2016
    Resource Type
  • Text
  • Collections this item is in
    Note
    • thesis
      Partial requirement for: M.A., Arizona State University, 2016
    • bibliography
      Includes bibliographical references (pages 46-47)
    • Field of study: Mathematics

    Citation and reuse

    Statement of Responsibility

    by Keenan Eikenberry

    Machine-readable links