Computing in arithmetic groups with Voronoï's algorithm.

DOI10.1016/j.jalgebra.2015.01.022zbMath1323.16014arXiv1407.6234OpenAlexW1988217051MaRDI QIDQ2344291

Oliver Braun, Renaud Coulangeon, Sebastian Schönnenbeck, Gabriele Nebe

Publication date: 13 May 2015

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.6234

zbMATH Keywords

presentationsgeneratorsword problemlatticesVoronoï algorithmmaximal ordersunit groups of orders

Mathematics Subject Classification ID

Computational aspects of associative rings (general theory) (16Z05) Units, groups of units (associative rings and algebras) (16U60) Quadratic forms (reduction theory, extreme forms, etc.) (11H55) Orders in separable algebras (16H10)

Related Items (10)

Equivalence of Lattice Orbit Polytopes ⋮ Computing isomorphisms between lattices ⋮ The Farrell-Tate and Bredon homology for \(\operatorname{PSL}_4(\mathbb{Z})\) via cell subdivisions ⋮ Resolutions for unit groups of orders ⋮ The constructive membership problem for discrete two-generator subgroups of \(\operatorname{SL}_2(\mathbb{R})\) ⋮ The mod 2 cohomology rings of congruence subgroups in the Bianchi groups ⋮ Linear groups and computation ⋮ Presentations of groups acting discontinuously on direct products of hyperbolic spaces ⋮ Computing S-unit groups of orders ⋮ On Farrell-Tate cohomology of \(\operatorname{GL}_3\) over rings of quadratic integers

Uses Software

• Magma
• polymake

Cites Work

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• Dual Cones and the Voronoi Algorithm
• Applications of a Computer Implementation of Poincare's Theorem on Fundamental Polyhedra
• Hyperbolic Tessellations Associated to Bianchi Groups
• Enumerating perfect forms

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