C*-algebras of sofic shifts

dc.contributor.authorSamuel, Jonathan Niall
dc.contributor.supervisorPutnam, Ian F.
dc.date.accessioned2017-11-15T22:34:31Z
dc.date.available2017-11-15T22:34:31Z
dc.date.copyright1998en_US
dc.date.issued2017-11-15
dc.degree.departmentDepartment of Mathematics and Statisticsen_US
dc.degree.levelDoctor of Philosophy Ph.D.en_US
dc.description.abstractThis 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.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/8799
dc.languageEnglisheng
dc.language.isoenen_US
dc.rightsAvailable to the World Wide Weben_US
dc.subjectC*-algebrasen_US
dc.subjectOperator theoryen_US
dc.titleC*-algebras of sofic shiftsen_US
dc.typeThesisen_US

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