Dense images of the power maps in lie groups and minimal parabolic subgroups
New York Journal of Mathematics
In this note, we study the density of the images of the k-th power maps Pk: G → G given by g → gk, for a connected Lie group G. We characterize Pk (G) being dense in G in terms of the minimal parabolic subgroups of G. For a simply connected simple Lie group G, we characterize all integers k, for which Pk (G) has dense image in G. We show also that for a simply connected semisimple Lie group weak exponentiality is equivalent to the image of the squaring map being dense.
Mandal, Arunava, "Dense images of the power maps in lie groups and minimal parabolic subgroups" (2018). Journal Articles. 1477.