RT Journal Article
T1 Presentations of the unit group of an order in a non-split quaternion algebra
A1 Corrales Rodrigáñez, Carmen
A1 Jespers, Eric
A1 Leal, Guilherme
A1 Rio, Ángel del
AB 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 H(K) over an imaginary quadratic extension K of the rationals. We then apply this method to obtain a presentation for the unit group of H(Z[(1+root-7)/(2)]). As a consequence a presentation is discovered for the orthogonal group SO3(Z[(1+root-7)/(2)]). 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.
PB Elsvier
SN 0001-8708
YR 2004
FD 2004
LK https://hdl.handle.net/20.500.14352/49857
UL https://hdl.handle.net/20.500.14352/49857
LA eng
NO Onderzoeksraad of Vrije Universiteit Brussel, Fonds voor Wetenschappelijk Onderzoek (Flanders),
NO D.G.I.of Spain and Fundación Séneca of Murcia.
DS Docta Complutense
RD 10 abr 2025