Picard modular groups generated by complex reflections
| Autor: | Mark, Alice, Paupert, Julien, Polletta, David |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Computational Aspects of Discrete Subgroups of Lie Groups. :127-133 |
| ISSN: | 1098-3627 0271-4132 |
| DOI: | 10.1090/conm/783/15735 |
| Popis: | In this short note we use the presentations found in \cite{MP} and \cite{Po} to show that the Picard modular groups ${\rm PU}(2,1,\mathcal{O}_d)$ with $d=1,3,7$ (respectively the quaternion hyperbolic lattice ${\rm PSp}(2,1,\mathcal{H})$ with entries in the Hurwitz integer ring $\mathcal{H}$) are generated by complex (resp. quaternionic) reflections, and that the Picard modular groups ${\rm PU}(2,1,\mathcal{O}_d)$ with $d=2,11$ have an index 4 subgroup generated by complex reflections. Comment: 5 pages |
| Databáze: | OpenAIRE |
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