Kk. Park et Aa. Sahin, Even Kakutani equivalence via (alpha)over-right-arrow and (beta)over-right-arrow equivalence in Z(2), PAC J MATH, 201(1), 2001, pp. 205-221
We show that an even Kakutani equivalence class of Z(2) actions is "spanned
" by <(<alpha>)over right arrow> and <(<beta>)over right arrow> equivalence
classes where <(<alpha>)over right arrow> = {1 + alpha (1), 1 + alpha (2)}
, <(<beta>)over right arrow> = {1 + beta (1), 1 + beta (2)} and {1, alpha (
-1)(i), beta (-1)(i)} are rationally independent for i = 1, 2. Namely, give
n such vectors <(<alpha>)over right arrow> and <(<beta>)over right arrow> a
nd two evenly Kakutani equivalent Z(2) actions S and T, we show that U is <
(<alpha>)over right arrow> -equivalent to S and <(<beta>)over right arrow>
-equivalent to T.