$C^*$-algebras associated with presentations of subshifts
By Kengo Matsumoto. Documenta Mathematica, 2002
71 citations recorded by the source corpus.
A A-graph system is a labeled Bratteli diagram with an upward shift except the top vertices. We construct a continuous graph in the sense of V. Deaconu from a A-graph system. It yields a Renault's groupoid C*-algebra by following Deaconu's construction. The class of these C*-algebras generalize the class of C*-algebras associated with subshifts and hence the class of Cuntz-Krieger algebras. They are unital, nuclear, unique C*-algebras subject to operator relations encoded in the structure of the A-graph systems among generating partial isometries and projections. If the A-graph systems are irreducible (resp. aperiodic), they are simple (resp. simple and purely infinite). K-theory formulae of these C*-algebras are presented so that we know an example of a simple and purely infinite C*-algebra in the class of these C*-algebras that is not stably isomorphic to any Cuntz-Krieger algebra.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ea17265e3a2573d4869dc6fc456db7100f13db18
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Citations in the corpus
- Some remarks on the C^*-algebras associated with subshifts (2004, background): “8], [26]).”
- Continuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras (2007, unknown): “ algebra DA, that are studied in Section 7. The results of this paper will be generalized to more general subshifts and the C∗-algebras associated with the subshifts considered in [Ma1] (cf.[CM]) and [Ma3] in a forthcoming paper [Ma4]. Throughout the paper, we denote by Z+ and Nthe set of nonnegativ”