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Subshifts and \(C^*\)-algebras from one-counter codes. (English) Zbl 1187.37018

de Jeu, Marcel (ed.) et al., Operator structures and dynamical systems. Satellite conference of the 5th European congress of mathematics, Leiden, Netherlands, July 21–25, 2008. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4747-3/pbk). Contemporary Mathematics 503, 93-119 (2009).
Summary: 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.
For the entire collection see [Zbl 1179.37004].

MSC:

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