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Some remarks on the $$C^*$$-algebras associated with subshifts. (English) Zbl 1067.46045
Summary: We point out incorrect lemmas in some papers regarding the $$C^*$$-algebras associated with subshifts written by the second named author. To recover the incorrect lemmas and the affected main results, we describe an alternative construction of $$C^*$$-algebras associated with subshifts. The resulting $$C^*$$-algebras are generally different from the originally constructed $$C^*$$-algebras associated with subshifts and they fit the mentioned papers including the incorrect results. The simplicity conditions and the $$K$$-theory formulae for the originally constructed $$C^*$$-algebras are described. We also introduce a condition called (*) for subshifts such that under this condition the new $$C^*$$-algebras and the original $$C^*$$-algebras are canonically isomorphic to each other. We finally present a subshift for which the two kinds of algebras have different $$K$$-theory groups.

##### MSC:
 46L05 General theory of $$C^*$$-algebras 37B10 Symbolic dynamics 46L80 $$K$$-theory and operator algebras (including cyclic theory) 47L35 Nest algebras, CSL algebras
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