Non-abelian extensions of minimal rotations
Tom 117 / 2009
Colloquium Mathematicum 117 (2009), 1-17 MSC: Primary 37B05, 37B20. DOI: 10.4064/cm117-1-1
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.