Speedups And Orbit Equivalence Of Finite Extensions Of Ergodic Zᵈ-Actions

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New York Journal Of Mathematics


We classify n-point extensions of ergodic Zᵈ-actions up to relative orbit equivalence and establish criteria under which one n-point extension of an ergodic Zᵈ-action can be sped up to be relatively isomorphic to an n-point extension of another ergodic Zᵈ-action. Both results are characterized in terms of an algebraic object associated to each n-point extension which is a conjugacy class of subgroups of the symmetric group on n elements.


ergodic Zᵈ action, finite extension, cocycle, speedup, relative isomorphism