Reference : On units in orders in 2-by-2 matrices over quaternion algebras with rational center |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/45733 | |||

On units in orders in 2-by-2 matrices over quaternion algebras with rational center | |

English | |

Kiefer, Ann [University of Luxembourg > Faculty of Humanities, Education and Social Sciences (FHSE) > LUCET] | |

2020 | |

Groups, Geometry, and Dynamics | |

14 | |

1 | |

213--242 | |

Yes | |

1661-7207 | |

1661-7215 | |

[en] Hyperbolic Geometry ; Presentation ; Clifford Algebra ; Quaternion Algebra ; Group Rings ; Unit Group | |

[en] We generalize an algorithm established in earlier work [21] to compute finitely
many generators for a subgroup of finite index of an arithmetic group acting properly discon- tinuously on hyperbolic space of dimension 2 and 3, to hyperbolic space of higher dimensions using Clifford algebras. We hence get an algorithm which gives a finite set of generators of finite index subgroups of a discrete subgroup of Vahlenâ€™s group, i.e. a group of 2-by-2 matrices with entries in the Clifford algebra satisfying certain conditions. The motivation comes from units in integral group rings and this new algorithm allows to handle unit groups of orders in 2-by-2 matrices over rational quaternion algebras. The rings investigated are part of the so-called exceptional components of a rational group algebra. | |

http://hdl.handle.net/10993/45733 | |

10.4171/ggd/541 |

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