Subshifts and 𝐶*-algebras from one-counter codes

Abstract

We introduce a class of subshifts under the name of "standard one-counter shifts ". The standard one-counter shifts are the Markov coded systems of certain Markov codes that belong to the family of one-counter languages. We study topological conjugacy and flow equivalence of standard one-counter shifts. To subshifts there are associated C*-algebras by their λgraph systems. We describe a class of standard one-counter shifts with the property that the C*-algebra associated to them is simple, while the C*-algebra that is associated to their inverse is not. This gives examples of subshifts that are not flow equivalent to their inverse. For a family of highly structured standard one-counter shifts we compute the K-groups.

A class of simpleC*-algebras arising from certain non-sofic subshifts

“…For N = 1, the subshift Z 1 is nothing but the subshift Z named as the context free shift in [23,Example 1.2.9] and the associated C * -algebra O Z1 is the C * -algebra O Z studied in [26]. For other type of coded systems, see for example [21].…”