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Unital shift equivalence

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arxiv 2504.09889 v1 pith:4MFBO5RI submitted 2025-04-14 math.DS math.OA

Kevin Aguyar Brix , Efren Ruiz This is my paper · ORCID
classification math.DSmath.OA
keywords shiftunitalequivalenceequivalentmatricesfiniteisomorphicone-sided
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We introduce and study a unital version of shift equivalence for finite square matrices over the nonnegative integers. In contrast to the classical case, we show that unital shift equivalence does not coincide with one-sided eventual conjugacy. We also prove that unital shift equivalent matrices define one-sided shifts of finite type that are continuously orbit equivalent. Consequently, unitally shift equivalent matrices have isomorphic topological full groups and isomorphic Leavitt path algebras, the latter being related to Hazrat's graded classification conjecture in algebra.

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  1. Geometric Methods for Stochastic Dynamical Systems

    math.DS 2026-07 conditional novelty 3.0 of 10

    A textbook-style synthesis claiming that the most probable transition path, the Schrödinger bridge, and α-divergence information geodesics are one geometric idea in the space of probability densities.

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