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arXiv · 1210.1386

Decomposition rank of Z-stable C*-algebras

Aaron Tikuisis·Wilhelm Winter
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Abstract

We show that C*-algebras of the form C(X) \otimes 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 the second named author, 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. 2012-10-04. Decomposition rank of Z-stable C*-algebras. https://doi.org/10.2140/apde.2014.7.673

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