We consider continuous extensions of minimal rotations on a locally connected compact group X by cocycles taking values in locally compact Lie groups and prove regularity (i.e. the existence of orbit closures which project onto the whole basis X) in certain special situations beyond the nilpotent case. We further discuss an open question on cocycles acting on homogeneous spaces which seems to be the missing key for a general regularity theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-1-1,
author = {Ulrich Hab\"ock and Vyacheslav Kulagin},
title = {Non-abelian extensions of minimal rotations},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {1-17},
zbl = {1180.37012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-1-1}
}
Ulrich Haböck; Vyacheslav Kulagin. Non-abelian extensions of minimal rotations. Colloquium Mathematicae, Tome 116 (2009) pp. 1-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-1-1/