C*-algebras of sofic shifts
| dc.contributor.author | Samuel, Jonathan Niall | |
| dc.contributor.supervisor | Putnam, Ian F. | |
| dc.date.accessioned | 2017-11-15T22:34:31Z | |
| dc.date.available | 2017-11-15T22:34:31Z | |
| dc.date.copyright | 1998 | en_US |
| dc.date.issued | 2017-11-15 | |
| dc.degree.department | Department of Mathematics and Statistics | en_US |
| dc.degree.level | Doctor of Philosophy Ph.D. | en_US |
| dc.description.abstract | 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. | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/8799 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights | Available to the World Wide Web | en_US |
| dc.subject | C*-algebras | en_US |
| dc.subject | Operator theory | en_US |
| dc.title | C*-algebras of sofic shifts | en_US |
| dc.type | Thesis | en_US |