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The uniqueness of Cuntz-Krieger type algebras
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Bernhard Burgstaller
Published/Copyright:
May 17, 2006
Abstract
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.
Received: 2004-11-05
Revised: 2006-05-30
Published Online: 2006-05-17
Published in Print: 2006-05-01
© Walter de Gruyter
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Articles in the same Issue
- Traces of CM values of modular functions
- Représentations semi-stables de torsion dans le cas er < p − 1
- Zero cycles on a threefold with isolated singularities
- On the density of algebraic foliations without algebraic invariant sets
- Compactness of solutions to some geometric fourth-order equations
- Relative cohomology with respect to a Lefschetz pencil
- There are genus one curves of every index over every number field
- The uniqueness of Cuntz-Krieger type algebras
