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arXiv · 1812.04555

Decidability of flow equivalence and isomorphism problems for graph C*-algebras and quiver representations

Mike Boyle·Benjamin Steinberg
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Abstract

We note that the deep results of Grunewald and Segal on algorithmic problems for arithmetic groups imply the decidability of several matrix equivalence problems involving poset-blocked matrices over Z. Consequently, results of Eilers, Restorff, Ruiz and S{\o}rensen imply that isomorphism and stable isomorphism of unital graph C*-algebras (including the Cuntz-Krieger algebras) are decidable. One can also decide flow equivalence for shifts of finite type, and isomorphism of Z-quiver representations (i.e., finite diagrams of homomorphisms of finitely generated abelian groups).

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Mike Boyle, Benjamin Steinberg. 2018-12-11. Decidability of flow equivalence and isomorphism problems for graph C*-algebras and quiver representations. https://arxiv.org/abs/1812.04555

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