Bernhard Burgstaller
The uniqueness of Cuntz-Krieger type algebras
We introduce a class of C*-algebras which can be viewed as a generalization of the classical Cuntz-Krieger algebras. Our approach is based on a flexible “generators and relations”-concept. The main result is a canonical uniqueness theorem stating that the C*-algebras of this class are uniquely determined by their generators and relations. We can show that rank one Cuntz-Krieger algebras with infinitely large transition matrices fall in this class, and this provides an alternative proof of a result of Exel and Laca. Further we analyze a subclass of rank two Cuntz-Krieger algebras inspired by shifts of finite type in dimension two, with an infinite set of generators and relations.
Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter
Print ISSN: 0075-4102
Volume: 2006, 05/2006
Pages: 207 - 236
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