Geodesic
Simple purely infinite $C^*$-algebras associated with normal subshifts
Documenta mathematica, Tome 28 (2023) no. 3, pp. 603-669

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We will introduce the notion of normal subshift. A subshift (Λ, σ) is said to be normal if it satisfies a certain synchronizing property called λ-synchronizing and is infinite as a set. There are many normal subshifts such as irreducible infinite sofic shifts, Dyck shifts, and β-shifts whose associated C∗-algebras are simple and purely infinite. Eventual conjugacy of one-sided normal subshifts and topological conjugacy of two-sided normal subshifts are characterized in terms of the associated C∗-algebras and the associated stabilized C∗-algebras with their diagonals and gauge actions, respectively.
DOI : 10.4171/dm/915
Classification : 37A55, 46L35, 37B10
Mots-clés : Subshifts, sofic shifts, normal subshifts, C∗-algebras, λ-graph systems 
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Kengo Matsumoto. Simple purely infinite $C^*$-algebras associated with normal subshifts. Documenta mathematica, Tome 28 (2023) no. 3, pp. 603-669. doi: 10.4171/dm/915

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