On inductive limits of matrix algebras over the two-torus

It will be shown in this paper that certain real rank zero C*-algebras which are inductive limits of C*-algebras of the form ⊕_i M_ki(C([inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /])) can be expressed as inductive limits of C*-algebras of the form ⊕_i M_ki(C(S¹)). In particular, if both A and B are of real rank zero and are inductive limits of C*-algebras of the form ⊕_i M_ki(C(S¹)), then also A ⊗ B is an inductive limit of C*-algebras of the form ⊕_i M_ki(C(S¹)). (Hence, A ⊗ B can be classified by its K-theory.) This is a key step in the general classification theory of inductive limit C*-algebras.