Subshifts and C*-algebras from one-counter codes

zbMATH Open1187.37018arXiv0910.4719MaRDI QIDQ5188446

Kengo Matsumoto, Wolfgang Krieger

Publication date: 10 March 2010

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 $lambda$-graph 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.

Full work available at URL: https://arxiv.org/abs/0910.4719

zbMATH Keywords

synchronization\(C^*\)-algebrasflow equivalencefinite alphabet\(K\)-groups\(\lambda\)-graph systemsMarkov codesstandard one-counter shifts

Mathematics Subject Classification ID

Formal languages and automata (68Q45) (K)-theory and operator algebras (including cyclic theory) (46L80) Symbolic dynamics (37B10)

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