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A Short Return to Simple Ah-Algebras with Real Rank Zero

Huaxin Lin

Abstract


Let $A$ be a unital simple AH-algebra with stable rank one and real rank zero such that $kx=0$ for all $x\in\operatorname{ker}\rho_A$, the subgroup of infinitesmal elements in $K_0(A)$, and for the same integer $k\ge 1$. We show that $A$ has tracial rank zero and is isomorphic to a unital simple AH-algebra with no dimension growth.

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DOI: http://dx.doi.org/10.7146/math.scand.a-17111

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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