Locally Ah-algebras (Memoirs of the American Mathematical Society) by Huaxin Lin (PDF)

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A unital separable $Cast$-algebra, $A$ is said to be locally AH with no dimension growth if there is an integer $d0$ satisfying the following: for any $epsilon 0$ and any compact subset $mathcal Fsubset A,$ there is a unital $Cast$-subalgebra, $B$ of $A$ with the form $PC(X, Mn)P$, where $X$ is a compact metric space with covering dimension no more than $d$ and $Pin C(X, Mn)$ is a projection, such that $mathrmdist(a, B)The authors prove that the class of unital separable simple $Cast$-algebras which are locally AH with no dimension growth can be classified up to isomorphism by their Elliott invariant. As a consequence unital separable simple $Cast$-algebras which are locally AH with no dimension growth are isomorphic to a unital simple AH-algebra with no dimension growth.

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