Decomposition rank of Z -stable C ∗ -algebras

Aaron Peter Tikuisis, Wilhelm Winter

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16 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)673-700
Number of pages28
JournalAnalysis & PDE
Volume7
Issue number3
DOIs
Publication statusPublished - 18 Jun 2014

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Keywords

  • nuclear C ∗ -algebras
  • decomposition rank
  • nuclear dimension
  • Jiang-Su algebra
  • classification
  • C(X)-algebras

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