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Decidability of the isomorphism problem for stationary AF-algebras and the associated ordered simple dimension groups

Ola Bratteli·Palle E. T. Jorgensen·Ki Hang Kim·Fred Roush
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Abstract

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.

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Ola Bratteli, Palle E. T. Jorgensen, Ki Hang Kim, Fred Roush. 2000-08-02. Decidability of the isomorphism problem for stationary AF-algebras and the associated ordered simple dimension groups. https://doi.org/10.1017/s014338570100178x 10.1017/s0143385702000044 10.1017/s0143385702000317

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