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arXiv · 1406.0883

High-dimensional Z-stable AH algebras

Aaron Tikuisis
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Abstract

It is shown that a C*-algebra of the form C(X,U), where U is a UHF algebra, is not an inductive limit of subhomogeneous 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)) $\leq$ 2.

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Aaron Tikuisis. 2014-06-03. High-dimensional Z-stable AH algebras. https://doi.org/10.1016/j.jfa.2015.05.013

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