Geodesic
SKEW PRODUCTS IN THE CENTRALIZER OF COMPACT ABELIAN GROUP EXTENSIONS
Acta mathematica Universitatis Comenianae, Tome 68 (1999) no. 1 
G. R. Goodson. SKEW PRODUCTS IN THE CENTRALIZER OF COMPACT ABELIAN GROUP EXTENSIONS. Acta mathematica Universitatis Comenianae, Tome 68 (1999) no. 1. http://geodesic.mathdoc.fr/item/AMUC_1999_68_1_a13/
@article{AMUC_1999_68_1_a13,
     author = {G. R. Goodson},
     title = {SKEW {PRODUCTS} {IN} {THE} {CENTRALIZER} {OF} {COMPACT} {ABELIAN} {GROUP} {EXTENSIONS}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {1999},
     volume = {68},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_1999_68_1_a13/}
}
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Voir la notice de l'article provenant de la source Comenius University

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.