Anderson and Putnam, and Kellendonk discovered methods of defining a C*- algebra on a noncommutative space associated with a tiling. The method employed was to use Renault's theory of groupoid C*-algebras of an equivalence relation on the tiling metric space. C*-algebras of a tiling have two purposes, on one hand they reveal information about the long range order of the tiling and on the other hand they provide interesting examples of C*-algebras. However, the two constructions do not include tilings such as the pinwheel tiling, with tiles appearing in an infinite number of orientations. We rectify this deficiency, with many interesting results appearing in the process.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/776 |
| Date | 10 April 2008 |
| Creators | Whittaker, Michael Fredrick. |
| Contributors | Putnam, Ian Fraser. |
| Source Sets | University of Victoria |
| Detected Language | English |
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