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Arunava Mandal
Dense images of the power maps in Lie groups and minimal parabolic subgroups view print
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| Published: |
February 14, 2018 |
| Keywords: |
Power maps of Lie groups, minimal parabolic subgroups, weak exponentiality |
| Subject: |
22E15 |
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Abstract
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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| Acknowledgements
The author thanks the IRCC for providing financial support for this study.
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| Author information
Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Delhi Centre, 7, S.J.S. Sansanwal Marg, New Delhi 110 016, India.
a.arunavamandal@gmail.com
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