Commensurability classes of discrete arithmetic hyperbolic groups

Colin MacLachlan

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper we show that the commensurability classes of discrete arithmetic subgroups of Isom(H n ) of the simplest type, i.e., those coming from quadratic forms of signature (n,1) over totally real number fields, can be parametrised by isomorphisms classes of quaternion algebras. This is applied to some low dimensional examples to show the commensurability of certain Coxeter groups.

Original languageEnglish
Pages (from-to)767-785
Number of pages19
JournalGroups, Geometry and Dynamics
Volume5
Issue number4
DOIs
Publication statusPublished - 2011

Fingerprint

Arithmetic Groups
Hyperbolic Groups
Quaternion Algebra
Coxeter Group
Isomorphism Classes
Number field
Quadratic form
Signature
Subgroup
Class

Keywords

  • arithmetic groups
  • hyperbolic groups
  • quaternion algebras
  • Coxeter groups

Cite this

Commensurability classes of discrete arithmetic hyperbolic groups. / MacLachlan, Colin.

In: Groups, Geometry and Dynamics, Vol. 5, No. 4, 2011, p. 767-785.

Research output: Contribution to journalArticle

MacLachlan, Colin. / Commensurability classes of discrete arithmetic hyperbolic groups. In: Groups, Geometry and Dynamics. 2011 ; Vol. 5, No. 4. pp. 767-785.
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