Classification of AH algebras with finitely many ideals

Abstract

The class of AH algebras with the ideal property and no dimension growth is classified by the invariant inv(⋅). In this paper, we introduce a new invariant, Inv(⋅), a refined version of inv(⋅) and show that they are equivalent for AH algebras with the ideal property and no dimension growth. Then we give a sufficient condition under which the Hausdorffified algebraic K1 group could be recovered from the traditional Elliott invariant. As an application, the class of AH algebras with the ideal property, no dimension growth, and finitely many ideals can be classified by the extended Elliott invariant.