Simple c*-algebras arising from β-expansion of real numbers

Yoshikazu Katayama, Kengo Matsumoto, Yasuo Watatani

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

Given a real number β > 1, we construct a simple purely infinite C*-algebra script O signβ as a C*-algebra arising from the β-subshift in the symbolic dynamics. The C*-algebras {script O signβ}1<β∈ℝ interpolate between the Cuntz algebras {script O signn}1<n∈ℕ. The K-groups for the C*-algebras script O signβ, 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 signβ is unique at the inverse temperature log β. which is the topological entropy for the β-shift. Moreover, script O signβ 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 languageEnglish
Pages (from-to)937-962
Number of pages26
JournalErgodic Theory and Dynamical Systems
Volume18
Issue number4
DOIs
Publication statusPublished - Jan 1 1998

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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