Abstract
LetG be a simply connected nilpotent Lie group. IfK andH are closed connected subgroups which intersect only in the neutral element, the multiplicationK ×H √G is shown to be a proper mapping. Furthermore, we consider the operation ofK ×H onG given byg · (k, h)=k −1 gh. It is shown that, under certain assumptions, this operation is proper if and only if it is free. Under more restrictive assumptions, the quotientK∖G/H is diffeomorphic to an ℝn.
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Singhof, W. Topological properties of the multiplication in a nilpotent Lie group. Ann Glob Anal Geom 13, 185–196 (1995). https://doi.org/10.1007/BF01120333
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DOI: https://doi.org/10.1007/BF01120333