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

2004/12/07 by Huaxin Lin, Lin, Huaxin, Hiroki Matui +1
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.math/0412129

38 pages

arxiv created 2004/12/07 · arxiv updated 2009/12/01

Abstract

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 A\T-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.

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