Simple 𝐴𝐻-algebras of real rank zero

Lin, Huaxin

doi:10.1090/S0002-9939-03-06995-8

Simple $AH$-algebras of real rank zero
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by Huaxin Lin

Proc. Amer. Math. Soc. 131 (2003), 3813-3819

DOI: https://doi.org/10.1090/S0002-9939-03-06995-8

Published electronically: March 25, 2003

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Abstract:

Let $A$ be a unital simple $AH$-algebra with real rank zero. It is shown that if $A$ satisfies a so-called fundamental comparison property, then $A$ has tracial topological rank zero. Combining some previous results, it is shown that a unital simple $AH$-algebra with real rank zero, stable rank one and weakly unperforated $K_0(A)$ must have slow dimension growth.

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