Date of Award

2017

Publisher

North Dakota State University

Document Type

Dissertation

Degree Awarded

Doctor of Philosophy (PhD)

Program

Mathematics

Department

Mathematics

College

Science and Mathematics

Faculty Advisor

Duncan, Benton

Description

Graph C*-algebras are constructed using projections corresponding to the vertices of the graph, and partial isometries corresponding to the edges of the graph. Here, we use the gauge-invariant uniqueness theorem to first establish that the C*-algebra of a graph composed of a directed cycle with finitely many edges emitting away from that cycle is Mn+k(C(T)), where n is the length of the cycle and k is the number of edges emitting away. We use this result to establish the main results of the thesis, which pertain to maximally edge-colored directed graphs. We show that the C*-algebra of any finite maximally edge-colored directed graph is *Mn(C){ Mn(C(T))}k, where n is the number of vertices of the graph and k depends on the structure of the graph. Finally, we show that this algebra is in fact isomorphic to Mn(*C{ C(T)}k).

Rights

NDSU Policy 190.6.2

Rights Link

https://www.ndsu.edu/fileadmin/policy/190.pdf

Handle Identifier

https://hdl.handle.net/10365/28666

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