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Abstract: We prove that the C*-algebra of a minimal diffeomorphism satisfiesBlackadar-s Fundamental Comparability Property for positive elements. Thisleads to the classification, in terms of K-theory and traces, of theisomorphism classes of countably generated Hilbert modules over such algebras,and to a similar classification for the closures of unitary orbits ofself-adjoint elements. We also obtain a structure theorem for the Cuntzsemigroup in this setting, and prove a conjecture of Blackadar and Handelman:the lower semicontinuous dimension functions are weakly dense in the space ofall dimension functions. These results continue to hold in the broader settingof unital simple ASH algebras with slow dimension growth and stable rank one.Our main tool is a sharp bound on the radius of comparison of a recursivesubhomogeneous C*-algebra. This is also used to construct uncountably manynon-Morita-equivalent simple separable amenable C*-algebras with the sameK-theory and tracial state space, providing a C*-algebraic analogue of McDuff-suncountable family of II 1 factors. We prove in passing that the range of theradius of comparison is exhausted by simple C*-algebras.

Autor: Andrew S. Toms



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