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

Aloys Krieg; Joana Rodriguez; Annalena Wernz

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

Number Theory 2019-01-18 v4

Authors: Aloys Krieg , Joana Rodriguez , Annalena Wernz

Abstract

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 $SO(1,3)$ .

Keywords

imaginary quadratic number field ring of integers maximal discrete extension sl2 atkin-lehner involution so(1,3)

Cite

@article{arxiv.1811.08251,
  title  = {The maximal discrete extension of $SL_2(\mathcal{\scriptstyle{O}}_K)$ for an imaginary-quadratic number field $K$},
  author = {Aloys Krieg and Joana Rodriguez and Annalena Wernz},
  journal= {arXiv preprint arXiv:1811.08251},
  year   = {2019}
}

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6 pages

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

Abstract

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