Full metadata
Title
C*-correspondences and topological dynamical systems associated to generalizations of directed graphs
Description
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. I introduce a "compactly aligned" condition for such product systems of graphs and show that this coincides with the similarly-named conditions for topological k-graphs and for the associated product systems over N^k of C*-correspondences. Finally I consider the constructions arising from topological dynamical systems consisting of a locally compact Hausdorff space and k commuting local homeomorphisms. I show that in this case, the associated topological k-graph correspondence is isomorphic to the product system over N^k of C*-correspondences arising from a related Exel-Larsen system. Moreover, I show that the topological k-graph C*-algebra has a crossed product structure in the sense of Larsen.
Date Created
2011
Contributors
- Patani, Nura (Author)
- Kaliszewski, Steven (Thesis advisor)
- Quigg, John (Thesis advisor)
- Bremner, Andrew (Committee member)
- Kawski, Matthias (Committee member)
- Spielberg, John (Committee member)
- Arizona State University (Publisher)
Topical Subject
Resource Type
Extent
vii, 104 p. : ill. (some col.)
Language
eng
Copyright Statement
In Copyright
Primary Member of
Peer-reviewed
No
Open Access
No
Handle
https://hdl.handle.net/2286/R.I.9202
Statement of Responsibility
by Nura Patani
Description Source
Retrieved on Oct. 3, 2012
Level of coding
full
Note
thesis
Partial requirement for: Ph.D., Arizona State University, 2011
bibliography
Includes bibliographical references (p. 100-104)
Field of study: Mathematics
System Created
- 2011-08-12 04:41:19
System Modified
- 2021-08-30 01:52:57
- 3 years 2 months ago
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