Geodesic
A lambda-graph system for the Dyck shift and its $K$-groups
Documenta mathematica, Tome 8 (2003), pp. 79-96.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $\lambda$-graph systems the term $\lq $Cantor horizon$\rq $ is proposed. The Dyck shifts are Cantor horizon. The $C^*$-algebras that are obtained from the Cantor horizon $\lambda$-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 $\lambda$-graph systems of the Dyck shifts are computed and it is found that the $K_0$-groups are not finitely generated.
Classification : 37B10, 46L35
Keywords: subshift, Shannon graph, $\lambda$-graph system, Dyck shift, K-groups, $C^*$-algebra 
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     author = {Krieger, Wolfgang and Matsumoto, Kengo},
     title = {A lambda-graph system for the {Dyck} shift and its $K$-groups},
     journal = {Documenta mathematica},
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     year = {2003},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2003__8__a14/}
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Krieger, Wolfgang; Matsumoto, Kengo. A lambda-graph system for the Dyck shift and its $K$-groups. Documenta mathematica, Tome 8 (2003), pp. 79-96. http://geodesic.mathdoc.fr/item/DOCMA_2003__8__a14/