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Algebraic shift equivalence and primitive matrices


Authors: Mike Boyle and David Handelman
Journal: Trans. Amer. Math. Soc. 336 (1993), 121-149
MSC: Primary 58F03; Secondary 28D20, 46L99, 54H20
DOI: https://doi.org/10.1090/S0002-9947-1993-1102219-4
MathSciNet review: 1102219
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Abstract: Motivated by symbolic dynamics, we study the problem, given a unital subring $ S$ of the reals, when is a matrix $ A$ algebraically shift equivalent over $ S$ to a primitive matrix? We conjecture that simple necessary conditions on the nonzero spectrum of $ A$ are sufficient, and establish the conjecture in many cases. If $ S$ is the integers, we give some lower bounds on sizes of realizing primitive matrices. For Dedekind domains, we prove that algebraic shift equivalence implies algebraic strong shift equivalence.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1102219-4
Article copyright: © Copyright 1993 American Mathematical Society

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