High-dimensional Z-stable AH algebras

Aaron Tikuisis

Research output: Contribution to journalArticle

3 Citations (Scopus)
4 Downloads (Pure)

Abstract

It is shown that a C⁎C⁎-algebra of the form C(X,U)C(X,U), where U is a UHF algebra, is not an inductive limit of subhomogeneous C⁎C⁎-algebras of topological dimension less than that of X . This is in sharp contrast to dimension-reduction phenomenon in (i) simple inductive limits of such algebras, where classification implies low-dimensional approximations, and (ii) when dimension is measured using decomposition rank, as the author and Winter proved that dr(C(X,U))≤2dr(C(X,U))≤2.
Original languageEnglish
Pages (from-to)2171-2186
Number of pages16
JournalJournal of Functional Analysis
Volume269
Issue number7
Early online date10 Jun 2015
DOIs
Publication statusPublished - 1 Oct 2015

Keywords

  • nuclear C*-algebras
  • decomposition rank
  • Jiang–Su algebra
  • approximately homogenous C* algebras

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