Archiv der Mathematik

, Volume 113, Issue 1, pp 37–41 | Cite as

The maximal discrete extension of \(SL_2(\mathcal {\scriptstyle {O}}_K)\) for an imaginary quadratic number field K

  • Aloys KriegEmail author
  • Joana Rodriguez
  • Annalena Wernz


Let \(\mathcal {\scriptstyle {O}}_K\) be the ring of integers of an imaginary quadratic number field K. In this paper we give a new description of the maximal discrete extension of the group \(SL_2(\mathcal {\scriptstyle {O}}_K)\) inside \(SL_2(\mathbb {C})\), which uses generalized Atkin–Lehner involutions. Moreover we find a natural characterization of this group in SO(1, 3).


Discrete groups Maximal discrete extension Atkin–Lehner involution. 

Mathematics Subject Classification



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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Lehrstuhl A für MathematikRWTH Aachen UniversityAachenGermany

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