Dense images of the power maps in lie groups and minimal parabolic subgroups

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Research Article

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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.

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