Some remarks on the $C^*$-algebras associated with subshifts

Authors

  • Toke Meier Carlsen
  • Kengo Matsumoto

DOI:

https://doi.org/10.7146/math.scand.a-14453

Abstract

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.

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Published

2004-09-01

How to Cite

Meier Carlsen, T., & Matsumoto, K. (2004). Some remarks on the $C^*$-algebras associated with subshifts. MATHEMATICA SCANDINAVICA, 95(1), 145–160. https://doi.org/10.7146/math.scand.a-14453

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Section

Articles