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

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

2004-12-07

arxiv.org/abs/math/0412129v1

Mathematics

Operator Algebras

38 pages

Scientific paper

Let $X$ be the Cantor set and $\phi$ be a minimal homeomorphism on $X\times\T$. We show that the crossed product $C^*$-algebra $C^*(X\times\T,\phi)$ is a simple $A\T$-algebra provided that the associated cocycle takes its values in rotations on $\T$. Given two minimal systems $(X\times\T,\phi)$ and $(Y\times\T,\psi)$ such that $\phi$ and $\psi$ 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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