Reference : On units in orders in 2-by-2 matrices over quaternion algebras with rational center
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/45733
On units in orders in 2-by-2 matrices over quaternion algebras with rational center
English
Kiefer, Ann mailto [University of Luxembourg > Faculty of Humanities, Education and Social Sciences (FHSE) > LUCET]
2020
Groups, Geometry, and Dynamics
14
1
213--242
Yes
1661-7207
1661-7215
[en] Hyperbolic Geometry ; Presentation ; Clifford Algebra ; Quaternion Algebra ; Group Rings ; Unit Group
[en] We generalize an algorithm established in earlier work [21] to compute finitely
many generators for a subgroup of finite index of an arithmetic group acting properly discon-
tinuously on hyperbolic space of dimension 2 and 3, to hyperbolic space of higher dimensions
using Clifford algebras. We hence get an algorithm which gives a finite set of generators
of finite index subgroups of a discrete subgroup of Vahlen’s group, i.e. a group of 2-by-2
matrices with entries in the Clifford algebra satisfying certain conditions. The motivation
comes from units in integral group rings and this new algorithm allows to handle unit groups
of orders in 2-by-2 matrices over rational quaternion algebras. The rings investigated are
part of the so-called exceptional components of a rational group algebra.
http://hdl.handle.net/10993/45733
10.4171/ggd/541

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