A lambda-graph system for the Dyck shift and its $K$-groups
Wolfgang Krieger, Kengo Matsumoto · Documenta Mathematica · 2003
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.