High-dimensional Z-stable AH algebras

Aaron Tikuisis

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2 Citations (Scopus)
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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

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High-dimensional
Inductive Limit
Algebra
Dimension Reduction
Imply
Decompose
Approximation

Keywords

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

Cite this

High-dimensional Z-stable AH algebras. / Tikuisis, Aaron.

In: Journal of Functional Analysis, Vol. 269, No. 7, 01.10.2015, p. 2171-2186.

Research output: Contribution to journalArticle

Tikuisis, Aaron. / High-dimensional Z-stable AH algebras. In: Journal of Functional Analysis. 2015 ; Vol. 269, No. 7. pp. 2171-2186.
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