Minimal dynamical systems on the product of the Cantor set and the circle II

• Huaxin Lin ^[1] ; Hiroki Matui ^[2]
  1. [1] East China Normal University

     East China Normal University

     China

     
  2. [2] Chiba University

     Chiba University

     Chūō-ku, Japón

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 12, Nº. 2, 2006, págs. 199-239
• Idioma: inglés
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• Resumen

  • Let X be the Cantor set and ϕ be a minimal homeomorphism on X ×T. We show that the crossed product C ∗ -algebra C ∗ (X ×T, ϕ) is a simple AT-algebra provided that the associated cocycle takes its values in rotations on T. Given two minimal systems (X ×T, ϕ) and (Y ×T, ψ) such that ϕ and ψ arise from cocycles with values in isometric homeomorphisms on T, we show that two systems are approximately K-conjugate when they have the same K-theoretical information.