abstract: C*-algebras of categories of paths were introduced by Spielberg in 2014 and generalize C*-algebras of higher rank graphs. An approximately finite dimensional (AF) C*-algebra is one which is isomorphic to an inductive limit of finite dimensional C*-algebras. In 2012, D.G. Evans and A. Sims proposed an analogue of a cycle for higher rank graphs and show that the lack of such an object is necessary for the associated C*-algebra to be AF. Here, I give a class of examples of categories of paths whose associated C*-algebras are Morita equivalent to a large number of periodic continued fraction AF algebras, first described by Effros and Shen in 1980. I then provide two examples which show that the analogue of cycles proposed by Evans and Sims is neither a necessary nor a sufficient condition for the C*-algebra of a category of paths to be AF. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2020
| Identifer | oai:union.ndltd.org:asu.edu/item:57148 |
| Date | January 2020 |
| Contributors | Mitscher, Ian (Author), Spielberg, John (Advisor), Bremner, Andrew (Committee member), Kalizsewski, Steven (Committee member), Kawski, Matthias (Committee member), Quigg, John (Committee member), Arizona State University (Publisher) |
| Source Sets | Arizona State University |
| Language | English |
| Detected Language | English |
| Type | Doctoral Dissertation |
| Format | 131 pages |
| Rights | http://rightsstatements.org/vocab/InC/1.0/ |
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