Presentations of the unit group of an order in a non-split quaternion algebra.

DOI10.1016/j.aim.2003.07.015zbMath1053.16024OpenAlexW2080694865MaRDI QIDQ1877890

Guilherme Leal, Capi Corrales-Rodrigáñez, Ángel Del Río, Eric Jespers

Publication date: 19 August 2004

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2003.07.015

zbMATH Keywords

ordersalgorithmspresentationsquaternion algebrasunit groupsfinite sets of generators

Mathematics Subject Classification ID

Group rings (16S34) Generators, relations, and presentations of groups (20F05) Units and factorization (11R27) Finite-dimensional division rings (16K20) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Units, groups of units (associative rings and algebras) (16U60)

Related Items (12)

GENERATORS OF ARITHMETIC QUATERNION GROUPS AND A DIOPHANTINE PROBLEM ⋮ Hyperbolic unit groups and quaternion algebras. ⋮ Groups of units of integral group rings commensurable with direct products of free-by-free groups. ⋮ Rotations and units in quaternion algebras ⋮ Macfarlane hyperbolic 3-manifolds ⋮ Group algebras of Kleinian type and groups of units. ⋮ Nonuniform Fuchsian codes for noisy channels ⋮ From the Poincaré Theorem to generators of the unit group of integral group rings of finite groups ⋮ A classification of exceptional components in group algebras over abelian number fields ⋮ Presentations of groups acting discontinuously on direct products of hyperbolic spaces ⋮ Computing in arithmetic groups with Voronoï's algorithm. ⋮ Computing arithmetic Kleinian groups

Cites Work

• Units of classical orders: A survey
• Units in skew fields
• Generators and relations for certain special linear groups
• On the representation of \(-1\) as a sum of two-squares in an algebraic number field
• Applications of a Computer Implementation of Poincare's Theorem on Fundamental Polyhedra
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