Computing in arithmetic groups with Voronoï's algorithm
Language
en
Article de revue
This item was published in
Journal of Algebra. 2015-08-01, vol. 435, p. 263–285
Elsevier
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Unit groups of orders
Generators
Presentation
Word problem
Lattices
Voronoï's algorithm
Origin
Hal imported