### Abstract

Given a real number β > 1, we construct a simple purely infinite C*-algebra script O sign_{β} as a C*-algebra arising from the β-subshift in the symbolic dynamics. The C*-algebras {script O sign_{β}}_{1<β∈ℝ} interpolate between the Cuntz algebras {script O sign_{n}}_{1<n∈ℕ}. The K-groups for the C*-algebras script O sign_{β}, 1 < β ∈ ℝ, are computed so that they are completely classified up to isomorphism. We prove that the KMS-state for the gauge action on script O sign_{β} is unique at the inverse temperature log β. which is the topological entropy for the β-shift. Moreover, script O sign_{β} is realized to be a universal C*-algebra generated by n - 1 = [β] isometries and one partial isometry with mutually orthogonal ranges and a certain relation coming from the sequence of β-expansion of 1.

Original language | English |
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Pages (from-to) | 937-962 |

Number of pages | 26 |

Journal | Ergodic Theory and Dynamical Systems |

Volume | 18 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 1998 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Ergodic Theory and Dynamical Systems*,

*18*(4), 937-962. https://doi.org/10.1017/S0143385798108350