Decidability of the isomorphism problem for stationary AF-algebras and the associated ordered simple dimension groups
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The notion of isomorphism of stable AF-C*-algebras is considered in this paper in the case when the corresponding Bratteli diagram is stationary, i.e., is associated with a single square primitive nonsingular incidence matrix. C*-isomorphism induces an equivalence relation on these matrices, called C*-equivalence. We show that the associated isomorphism equivalence problem is decidable, i.e., there is an algorithm that can be used to check in a finite number of steps whether two given primitive nonsingular matrices are C*-equivalent or not.
55 pages, LaTeX2e (amsart class). In this version the main theorem has been extended to possibly singular primitive integer matrixes, and the clarity of the presentation has been improved substantially throughout the paper
55 pages, LaTeX2e (amsart class). In this version the main theorem has been extended to possibly singular primitive integer matrixes, and the clarity of the presentation has been improved substantially throughout the paper