Decomposition Rank of Z-stable C∗-algebras
نویسنده
چکیده
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 the second named author, even in a non-simple setting, and gives evidence that the topological dimension of noncommutative spaces is governed by fibres rather than base spaces.
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تاریخ انتشار 2012