High-dimensional Z-stable AH algebras
arXiv:1406.0883 · doi:10.1016/j.jfa.2015.05.013
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)) 2.
14 pages. Improved the main result to handle subhomogeneous approximations