Abstract

We show that an even Kakutani equivalence class of Z² actions is “spanned” by α and β equivalence classes where α = {1 + α₁,1 + α₂}, β = {1 + β₁,1 + β₂} and {1,α_i⁻¹,β_i⁻¹} are rationally independent for i = 1,2. Namely, given such vectors α and β and two evenly Kakutani equivalent Z² actions S and T, we show that U is α -equivalent to S and β -equivalent to T.

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