DOCUMENTA MATHEMATICA, Vol. 8 (2003), 79-96

Wolfgang Krieger and Kengo Matsumoto

A Lambda-Graph System for the Dyck Shift and Its K-Groups

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.

2000 Mathematics Subject Classification: Primary 37B10; Secondary 46L35.

Keywords and Phrases: subshift, Shannon graph, $\lambda$-graph system, Dyck shift, K-groups, $C^*$-algebra

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