Dimension groups for subshifts and simplicity of the associated C^*-algebras

抄録

We describe the notion of the dimension group for subshifts in terms of symbolic dynamical system and show that the dimension group is a conjugacy invariant. We will show that the the hereditary subsets invariant under the dimension group au-tomorphism exactly corresponds to the gauge invariant ideals of the associated C^*-algebra \mathcal{O}_Λ for the subshift (Λ, σ). As a result, we give the conditions that the C^*-algebra \mathcal{O}_Λ becomes simple and purely infinite in terms of symbolic dynamics.