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2014 Decomposition rank of $\mathcal{Z}$-stable $\mathrm{C}^*$-algebras
Aaron Tikuisis, Wilhelm Winter
Anal. PDE 7(3): 673-700 (2014). DOI: 10.2140/apde.2014.7.673

Abstract

We show that C-algebras of the form C(X)Z, where X is compact and Hausdorff and Z denotes the Jiang–Su algebra, have decomposition rank at most 2. This amounts to a dimension reduction result for C-bundles with sufficiently regular fibres. It establishes an important case of a conjecture on the fine structure of nuclear C-algebras of Toms and Winter, even in a nonsimple setting, and gives evidence that the topological dimension of noncommutative spaces is governed by fibres rather than base spaces.

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Aaron Tikuisis. Wilhelm Winter. "Decomposition rank of $\mathcal{Z}$-stable $\mathrm{C}^*$-algebras." Anal. PDE 7 (3) 673 - 700, 2014. https://doi.org/10.2140/apde.2014.7.673

Information

Received: 30 April 2013; Revised: 5 September 2013; Accepted: 4 October 2013; Published: 2014
First available in Project Euclid: 20 December 2017

MathSciNet: MR3227429
zbMATH: 1303.46048
Digital Object Identifier: 10.2140/apde.2014.7.673

Subjects:
Primary: 46L35, 46L85

Rights: Copyright © 2014 Mathematical Sciences Publishers

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