Degree Type

Dissertation

Date of Award

2003

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Justin R. Peters

Abstract

By utilizing the connections between C*-algebras, groupoids, and inverse semigroups, we obtain a characterization theorem, in terms of dynamical systems, of approximately finite-dimensional (AF) C*-algebras. The dynamical systems considered in this characterization consist of partially defined homeomorphisms, and our theorem is applied to obtain a result about crossed product C*-algebras. The ideas developed here are then used to compute the K-theory for AF algebras, and these K-theoretic calculations are applied to some specific examples of AF algebras. Finally, we show that for a given dimension group, a groupoid can be obtained directly from the dimension group's structure whose associated C*-algebra has K0 group isomorphic to the original dimension group.

DOI

https://doi.org/10.31274/rtd-180813-13219

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu

Copyright Owner

Ryan Jonathan Zerr

Language

en

Proquest ID

AAI3085962

File Format

application/pdf

File Size

76 pages

Included in

Mathematics Commons

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