|
|||||
|
|
Presentations of the unit group of an order in a non-split quaternion algebra |
|
| Authors: | Capi Corrales Eric Jespers |
| Affiliation: | a Facultad de Matemáticas, Universidad Complutense de Madrid, Madrid, Spain b Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium c Instituto de Matemática, Universidade Federal do Rio de Janeiro, 21910 Rio de Janeiro, Brazil d Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain |
| Abstract: | We give an algorithm to determine a finite set of generators of the unit group of an order in a non-split classical quaternion algebra  over an imaginary quadratic extension K of the rationals. We then apply this method to obtain a presentation for the unit group of  . As a consequence a presentation is discovered for the orthogonal group  . These results provide the first examples of a characterization of the unit group of some group rings that have an epimorphic image that is an order in a non-commutative division algebra that is not a totally definite quaternion algebra. |
| Keywords: | primary 16U60 secondary 11R27 16A26 |
| 本文献已被 ScienceDirect 等数据库收录！ | |