New York Journal of Mathematics
Volume 24 (2018) 201-209


Arunava Mandal

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

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Published: February 14, 2018
Keywords: Power maps of Lie groups, minimal parabolic subgroups, weak exponentiality
Subject: 22E15

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.


The author thanks the IRCC for providing financial support for this study.

Author information

Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Delhi Centre, 7, S.J.S. Sansanwal Marg, New Delhi 110 016, India.