ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 68,   1   (1999)
pp.   171-178

SKEW PRODUCTS IN THE CENTRALIZER OF COMPACT ABELIAN GROUP EXTENSIONS
G. R. GOODSON

Abstract.  If $T_\psi$ is an ergodic group extension of a weakly mixing transformation $T$ having minimal self-joinings, then it is shown that isomorphism between $T_\psi$ and its inverse implies isomorphism between $T$ and $T^-1$. However, if $T$ satisfies the weaker condition of being simple it is shown that that isomorphism between $T_\psi$ and its inverse does not imply the isomorphism between $T$ and $T^-1$. This answers a question asked by D. Rudolph.

AMS subject classification.  28D05; Secondary 47A35
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