This Dissertation shows how the theory of C*-algebra of graphs relates to the theory of C*-algebras of sofic shifts. C*-algebras of sofic shifts are generalizations of Cuntz-Krieger algebras [8]. It is shown that if X is a sofic shift, then the C*-algebra of the sofic shift, Oₓ, is isomorphic to the C*-algebra of a directed graph E, C *(E). The graph E is shown to be the well known past set presentation of X constructed in [13].
We focus on the consequences of this result: In particular uniqueness of the generators of Oₓ, pure infiniteness, and ideal structure of the algebra Oₓ. We show the existence of an ideal I ⊂ Oₓ such that when we form the quotient, Oₓ/I, it is isomorphic to C*( F), and F is the left Krieger cover graph of X—a well known, canonical graph one can associate with a sofic shift. The dual cover, the right Krieger cover, can also be related to the structure of Oₓ, and we illustrate this relationship.
Chapter 6 shows what happens when we label a directed graph E in a left resolving way. When the graph E and the labeling satisfy certain technical conditions, we can generate a C*-algebra Lₓ ⊂ C*(E), with Lₓ ≅ Oₓ provided that X an irreducible sofic shift. / Graduate
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/8799 |
| Date | 15 November 2017 |
| Creators | Samuel, Jonathan Niall |
| Contributors | Putnam, Ian F. |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
| Rights | Available to the World Wide Web |
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