High-dimensional Z-stable AH algebras

Aaron Tikuisis

doi:10.1016/j.jfa.2015.05.013

High-dimensional Z-stable AH algebras

Aaron Tikuisis

Mathematical Science

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

23 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 language	English
Pages (from-to)	2171-2186
Number of pages	16
Journal	Journal of Functional Analysis
Volume	269
Issue number	7
Early online date	10 Jun 2015
DOIs	https://doi.org/10.1016/j.jfa.2015.05.013
Publication status	Published - 1 Oct 2015

Keywords

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

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High-dimensional Z-stable AH algebras
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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.",

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AB - 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.

KW - nuclear C-algebras

KW - decomposition rank

KW - Jiang–Su algebra

KW - approximately homogenous C algebras

U2 - 10.1016/j.jfa.2015.05.013

DO - 10.1016/j.jfa.2015.05.013

M3 - Article

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VL - 269

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EP - 2186

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 7

ER -

High-dimensional Z-stable AH algebras

Abstract

Keywords

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