Some remarks on the C^*-algebras associated with subshifts - Meier Carlsen, Toke; Matsumoto, Kengo (MATHEMATICA SCANDINAVICA, 2004)
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 will 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.