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AN EMBEDDING THEOREM FOR QUATERNION ALGEBRAS

Published online by Cambridge University Press:  01 August 1999

TED CHINBURG  and
EDUARDO FRIEDMAN
TED CHINBURG
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104, USA; [email protected]
EDUARDO FRIEDMAN
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago 1, Chile; [email protected]
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Abstract

An integral version of a classical embedding theorem concerning quaternion algebras B over a number field k is proved. Assume that B satisfies the Eichler condition, that is, some infinite place of k is not ramified in B, and let Ω be an order in a quadratic extension of k. The maximal orders of B which admit an embedding of Ω are determined. Although most Ω embed into either all or none of the maximal orders of B, it turns out that some Ω are ‘selective’, in the sense that they embed into exactly half of the isomorphism types of maximal orders of B. As an application, the maximal arithmetic subgroups of B*/k* which contain a given element of B*/k* are determined.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 1 , August 1999 , pp. 33 - 44
Copyright
The London Mathematical Society 1999

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Footnotes

The first author was partially supported by NSF grant DMS92-01016 and by NSA grant MDA904-90-H-4033. The second author was partially supported by Fondecyt grant 196-0867 and European Union grant CI1*-CT93-0353.