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Decomposition rank of
$\mathcal{Z}$-stable $\mathrm{C}^*$-algebras
Aaron Tikuisis and Wilhelm Winter |
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Vol. 7 (2014), No. 3, 673–700
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Abstract |
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We show that -algebras of the form , where is compact and Hausdorff and denotes the Jiang–Su algebra, have decomposition rank at most . This amounts to a dimension reduction result for -bundles with sufficiently regular fibres. It establishes an important case of a conjecture on the fine structure of nuclear -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. |
Keywords
nuclear $\mathrm{C}^*$-algebras, decomposition rank,
nuclear dimension, Jiang–Su algebra, classification,
$C(X)$-algebras
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Mathematical Subject Classification 2010
Primary: 46L35, 46L85
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Milestones
Received: 30 April 2013
Revised: 5 September 2013
Accepted: 4 October 2013
Published: 18 June 2014
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Authors |
| Aaron Tikuisis | |
| Institute of Mathematics University of Aberdeen Fraser Noble Building Aberdeen AB24 3UE United Kingdom |
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| Wilhelm Winter | |
| Mathematisches Institut Universität Münster Einsteinstraße 62 D-48149 Münster Germany |
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