We consider the semigroup of principal integral ideals, P. in a number field and study its associated Toeplitz representation. From this specific representation, a certain covariance relation is obtained and subsequently arbitrary isometric representations of P which satisfy this relation are analyzed. This leads to the study of the universal C*-algebra C*(P) satisfying these relations and to the following results. We first express C*(P) as a crossed product of an abelian C*-algebra by endomorphisms associated to P. We then give an explicit characterization of faithful representations of this crossed product, from which it follows as an immediate corollary that the Toeplitz C*-algebra is in fact isomorphic to the universal C*-algebra.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/2380 |
| Date | 18 March 2010 |
| Creators | Peebles, Jason Samuel |
| Contributors | Laca, Marcelo |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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