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Nilpotent Lie groups and hyperbolic automorphisms

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Abstract

A connected Lie group admitting an expansive automorphism is known to be nilpotent, but not all nilpotent Lie groups admit expansive automorphisms. In this article, we find sufficient conditions for a class of nilpotent Lie groups to admit expansive automorphisms.

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Acknowledgements

The authors would like to thank Prof. S.G. Dani for suggesting [14], and Prof. E. Vinberg for pointing out the mistakes in the previous version. We also thank the referee of the current version for his suggestions in enriching the exposition. The first named author acknowledges the support of the National Board for Higher Mathematics (NBHM), India, and thanks the Indian Statistical Institute Bangalore Center for their hospitality during the author’s stay there as an NBHM post-doctoral fellow.

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Funding was provided by National Board for Higher Mathematics (Grant No. 2/40(8)/2016/R&D-II/5757).

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Correspondence to Manoj Choudhuri.

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Choudhuri, M., Raja, C.R.E. Nilpotent Lie groups and hyperbolic automorphisms. Arch. Math. 115, 247–255 (2020). https://doi.org/10.1007/s00013-020-01487-8

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