Abstract
Let \(\Gamma\) be a nonelementary discrete subgroup of \({\mathrm {Sp}}(n,1)\). We show that if the trace skew-field of \(\Gamma\) is commutative, then \(\Gamma\) stabilizes a copy of complex hyperbolic subspace of \({\mathbf {H}}^n_{{\mathbb {H}}}\).
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Acknowledgements
The authors thank an anonymous referee for helpful suggestions, including shorter proof of Theorem 1.2 (Remark 3.4). S. Kim gratefully acknowledges supports from the 2019 scientific promotion program by Jeju National University and the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B07043321). J. Kim was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2017R1C1B1003906).
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Kim, S., Kim, J. Quaternionic hyperbolic Kleinian groups with commutative trace skew-fields. Ann Glob Anal Geom 57, 455–464 (2020). https://doi.org/10.1007/s10455-020-09708-7
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DOI: https://doi.org/10.1007/s10455-020-09708-7