Presentations of the unit group of an order in a non-split quaternion algebra
| dc.contributor.author | Corrales Rodrigáñez, Carmen | |
| dc.contributor.author | Jespers, Eric | |
| dc.contributor.author | Leal, Guilherme | |
| dc.contributor.author | Rio, Ángel del | |
| dc.date.accessioned | 2023-06-20T09:32:36Z | |
| dc.date.available | 2023-06-20T09:32:36Z | |
| dc.date.issued | 2004 | |
| dc.description.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 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. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Onderzoeksraad of Vrije Universiteit Brussel, Fonds voor Wetenschappelijk Onderzoek (Flanders), | |
| dc.description.sponsorship | D.G.I.of Spain and Fundación Séneca of Murcia. | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/14942 | |
| dc.identifier.doi | 10.1016/j.aim.2003.07.015 | |
| dc.identifier.issn | 0001-8708 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0001870803002585 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/49857 | |
| dc.issue.number | 2 | |
| dc.journal.title | Advances in Mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 524 | |
| dc.page.initial | 498 | |
| dc.publisher | Elsvier | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512.54 | |
| dc.subject.keyword | Algorithms | |
| dc.subject.keyword | Finite sets of generators | |
| dc.subject.keyword | Unit groups | |
| dc.subject.keyword | Orders | |
| dc.subject.keyword | quaternion algebras | |
| dc.subject.keyword | Presentations | |
| dc.subject.ucm | Grupos (Matemáticas) | |
| dc.title | Presentations of the unit group of an order in a non-split quaternion algebra | |
| dc.type | journal article | |
| dc.volume.number | 186 | |
| dcterms.references | [1] A.F. Beardon, The Geometry of Discrete Groups, springer, Berlin, 1983. [2] L. Bianchi, Sui gruppi de sostituzioni lineari con coeficienti appartenenti a corpi quadratici imaginari, Math. Ann. 40 (1892) 332–412. [3] J. Elstrodt, F. Grunewald, J. Mennicke, Groups Acting on Hyperbolic Space, Harmonic Analysis and Number Theory, Springer, Berlin, 1998. [4] B. Fein, B. Gordon, J.M. Smith, On the representation of 1 as a sum of two squares in an algebraic number field, J. Number Theory 3 (1971) 310–315. [5] B. Fine, The Algebraic Theory of the Bianchi Groups, Marcel Dekker, New York, 1989. [6] A.J. Hahn, O.T. O’Meara, The Classical Groups and K-Theory, Grundlehren der mathematischen Wissenschaften 291, Springer, Heidelberg, 1989. [7] E. Jespers, Units in integral group rings: a survey, Proceedings of the International Conference on Methods in Ring Theory, Trento, 1997. Lecture Notes in Pure and Applied Mathematics, Vol. 198,Marcel Dekker, New York, 1998, pp. 141–169. [8] E. Kleinert, Units in Skew Fields, Progress in Mathematics, 186, Birkha¨ user Verlag, Basel, 2000. [9] E. Kleinert, Units of classical orders: a survey, Enseign. Math. (2) 40 (3–4) (1994) 205–248. [10] H. Poincare´, Me´moire sur les groupes kleine´ es, Acta. Math. 3 (1883) 49–92. [11] R. Riley, Applications of a computer implementation of Poincare´ ’s theorem on fundamental polyhedra, Math. Comp. 40 (162) (1983) 607–632. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 9a5ad1cc-287e-48b3-83f9-e3d1e36d5ff2 | |
| relation.isAuthorOfPublication.latestForDiscovery | 9a5ad1cc-287e-48b3-83f9-e3d1e36d5ff2 |
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