We will introduce the notion of normal subshift. A subshift (, ) is said to be normal if it satisfies a certain synchronizing property called -synchronizing and is infinite as a set. There are many normal subshifts such as irreducible infinite sofic shifts, Dyck shifts, and -shifts whose associated -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 -algebras and the associated stabilized -algebras with their diagonals and gauge actions, respectively.
Cite this article
Kengo Matsumoto, Simple purely infinite -algebras associated with normal subshifts. Doc. Math. 28 (2023), no. 3, pp. 603–669DOI 10.4171/DM/915