Commensurability classes of discrete arithmetic hyperbolic groups | Zendy

Colin M. MacLachlan | Zendy

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Commensurability classes of discrete arithmetic hyperbolic groups

Author(s) -

Colin M. MacLachlan

Publication year - 2011

Publication title -

groups geometry and dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.05

H-Index - 25

eISSN - 1661-7215

pISSN - 1661-7207

DOI - 10.4171/ggd/147

Subject(s) - commensurability (mathematics) , mathematics , arithmetic , pure mathematics , discrete group , algebra over a field , group (periodic table) , chemistry , organic chemistry

In this paper we show that the commensurability classes of discrete arithmetic subgroups of Isom.H/ 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. Mathematics Subject Classification (2010). 11F06, 11E88, 20G20.

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