Minimal dynamical systems on the product of the Cantor set and the circle II期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Huaxin Lin Hiroki Matui

Institution:	(1) Department of Mathematics, East China Normal University, Shanghai, China;(2) Department of Mathematics, University of Oregon, Eugene, OR 97403, USA;(3) Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan

Abstract:	Let X be the Cantor set and φ be a minimal homeomorphism on $X \times \mathbb{T}$ . We show that the crossed product C^-algebra $C(X \times \mathbb{T}, \varphi)$ is a simple A $\mathbb{T}$ -algebra provided that the associated cocycle takes its values in rotations on $\mathbb{T}$ . Given two minimal systems $(X \times \mathbb{T}, \varphi)$ and $(Y \times \mathbb{T}, \psi)$ such that φ and ψ arise from cocycles with values in isometric homeomorphisms on $\mathbb{T}$ , we show that two systems are approximately K-conjugate when they have the same K-theoretical information.

Keywords:	Primary 46L55 Secondary 54H20
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