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1 December 2017 The C∗-algebra of a minimal homeomorphism of zero mean dimension
George A. Elliott, Zhuang Niu
Duke Math. J. 166(18): 3569-3594 (1 December 2017). DOI: 10.1215/00127094-2017-0033

Abstract

Let X be an infinite metrizable compact space, and let σ:XX be a minimal homeomorphism. Suppose that (X,σ) has zero mean topological dimension. The associated C∗-algebra A=C(X)σZ is shown to absorb the Jiang–Su algebra Z tensorially; that is, AAZ. This implies that A is classifiable when (X,σ) is uniquely ergodic. Moreover, without any assumption on the mean dimension, it is shown that AA always absorbs the Jiang–Su algebra.

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George A. Elliott. Zhuang Niu. "The C∗-algebra of a minimal homeomorphism of zero mean dimension." Duke Math. J. 166 (18) 3569 - 3594, 1 December 2017. https://doi.org/10.1215/00127094-2017-0033

Information

Received: 8 March 2016; Revised: 11 April 2017; Published: 1 December 2017
First available in Project Euclid: 21 November 2017

zbMATH: 06837467
MathSciNet: MR3732883
Digital Object Identifier: 10.1215/00127094-2017-0033

Subjects:
Primary: 46L35
Secondary: ‎37B05‎ , 46L85

Keywords: C∗-algebras , classification of C∗-algebras , mean dimension , minimal homeomorphism

Rights: Copyright © 2017 Duke University Press

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Vol.166 • No. 18 • 1 December 2017
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