Abstract
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.
Citation
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