We show that semisimple actions of l.c.s.c. Abelian groups and cocycles with values in such groups can be used to build new examples of semisimple automorphisms (ℤ-actions) which are relatively weakly mixing extensions of irrational rotations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-1-3, author = {Mariusz Lema\'nczyk and Mieczys\l aw K. Mentzen and Hitoshi Nakada}, title = {Semisimple extensions of irrational rotations}, journal = {Studia Mathematica}, volume = {157}, year = {2003}, pages = {31-57}, zbl = {1019.37001}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-1-3} }
Mariusz Lemańczyk; Mieczysław K. Mentzen; Hitoshi Nakada. Semisimple extensions of irrational rotations. Studia Mathematica, Tome 157 (2003) pp. 31-57. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-1-3/