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 k i (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 k i (C( S 1 )). In particular, if both A and B are of real rank zero and are inductive limits of C*-algebras of the form ⊕ i M k i (C( S 1 )), then also A ⊗ B is an inductive limit of C*-algebras of the form ⊕ i M k i (C( S 1 )). (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.

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