Geodesic
A lambda-graph system for the Dyck shift and its $K$-groups
Documenta mathematica, Tome 8 (2003), pp. 79-96
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A property of subshifts is described that allows to associate to the subshift a distinguishied presentation by a compact Shannon graph. For subshifts with this property and for the resulting invariantly associated compact Shannon graphs and their λ-graph systems the term ‘Cantor horizon′ is proposed. The Dyck shifts are Cantor horizon. The C∗-algebras that are obtained from the Cantor horizon λ-graph systems of the Dyck shifts are separable, unital, nuclear, purely infinite and simple with UCT. The K-groups and Bowen-Franks groups of the Cantor horizon λ-graph systems of the Dyck shifts are computed and it is found that the K0​-groups are not finitely generated.
DOI : 10.4171/dm/139
Classification : 37B10, 46L35
Mots-clés : subshift, Shannon graph, λ-graph system, Dyck shift, K-groups, C∗-algebra 
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     author = {Wolfgang Krieger and Kengo Matsumoto},
     title = {A lambda-graph system for the {Dyck} shift and its $K$-groups},
     journal = {Documenta mathematica},
     pages = {79--96},
     year = {2003},
     volume = {8},
     doi = {10.4171/dm/139},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/139/}
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Wolfgang Krieger; Kengo Matsumoto. A lambda-graph system for the Dyck shift and its $K$-groups. Documenta mathematica, Tome 8 (2003), pp. 79-96. doi: 10.4171/dm/139

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