Classification of Cuntz-Krieger algebras up to stable isomorphism

✍ Scribed by Restorff, Gunnar

• Book ID: 118740326
• Publisher: Walter de Gruyter GmbH & Co. KG
• Year: 2006
• Tongue: English
• Weight: 272 KB
• Volume: 2006
• Category: Article
• ISSN: 0075-4102
• DOI: 10.1515/CRELLE.2006.074

✦ Synopsis

In this paper we classify all Cuntz-Krieger algebras whose adjacency matrices satisfy condition (II) of Cuntz. The invariant arises naturally from the ideal lattice and the six-term exact sequences from K-theory, while the proof of this invariant being complete depends on recent results on flow equivalence of shifts of finite type by Mike Boyle and Danrun Huang. r Shortly after Franks had made a successful classification of irreducible shifts of finite type up to flow equivalence ([9]), Cuntz raised the question of whether this invariant or the K 0 -group alone classifies simple Cuntz-Krieger algebras up to stable isomorphism. He sketched in [6] that it was enough to answer whether O 2 and O 2 À are isomorphic, where O 2 resp. O 2 À are the Cuntz-Krieger algebras associated to the matrices 1 1