Geodesic
Commensurability classes of discrete arithmetic hyperbolic groups
Colin Maclachlan1
1University of Aberdeen, UK
Groups, geometry, and dynamics, Tome 5 (2011) no. 4, pp. 767-785

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DOI

In this paper we show that the commensurability classes of discrete arithmetic subgroups of Isom(Hn) 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.
DOI : 10.4171/ggd/147
Classification : 11-XX, 20-XX, 00-XX
Mots-clés : Arithmetic groups, hyperbolic groups, quaternion algebras, Coxeter groups

Colin Maclachlan  1

1 University of Aberdeen, UK 
Colin Maclachlan. Commensurability classes of discrete arithmetic   hyperbolic groups. Groups, geometry, and dynamics, Tome 5 (2011) no. 4, pp. 767-785. doi: 10.4171/ggd/147
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     year = {2011},
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     number = {4},
     doi = {10.4171/ggd/147},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/147/}
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