Computing in arithmetic groups with Voronoï's algorithm
| hal.structure.identifier | Lehrstuhl II für Mathematik | |
| dc.contributor.author | BRAUN, Oliver | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | COULANGEON, Renaud | |
| hal.structure.identifier | Lehrstuhl II für Mathematik | |
| dc.contributor.author | NEBE, Gabriele | |
| hal.structure.identifier | Lehrstuhl II für Mathematik | |
| dc.contributor.author | SCHÖNNENBECK, Sebastian | |
| dc.date.accessioned | 2024-04-04T03:17:22Z | |
| dc.date.available | 2024-04-04T03:17:22Z | |
| dc.date.issued | 2015-08-01 | |
| dc.identifier.issn | 0021-8693 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194301 | |
| dc.description.abstractEn | We describe an algorithm, meant to be very general, to compute a presentation of the group of units of an order in a (semi-)simple algebra over QQ. Our method is based on a generalisation of Voronoï's algorithm for computing perfect forms, combined with Bass–Serre theory. It differs essentially from previously known methods to deal with such questions, e.g. for units in quaternion algebras. We illustrate this new algorithm by a series of examples where the computations are carried out completely. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | Unit groups of orders | |
| dc.subject.en | Generators | |
| dc.subject.en | Presentation | |
| dc.subject.en | Word problem | |
| dc.subject.en | Lattices | |
| dc.subject.en | Voronoï's algorithm | |
| dc.title.en | Computing in arithmetic groups with Voronoï's algorithm | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.jalgebra.2015.01.022 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Mathématiques [math]/Théorie des groupes [math.GR] | |
| dc.identifier.arxiv | 1407.6234 | |
| bordeaux.journal | Journal of Algebra | |
| bordeaux.page | 263–285 | |
| bordeaux.volume | 435 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01208022 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01208022v1 | |
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