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Presentations of the unit group of an order in a non-split quaternion algebra

Corrales Rodrigañez, Carmen and Jespers, Eric and Leal, Guilherme and Rio, Ángel del (2004) Presentations of the unit group of an order in a non-split quaternion algebra. Advances in Mathematics, 186 (2). pp. 498-524. ISSN 0001-8708

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Abstract

We give an algorithm to determine a finite set of generators of the unit group of an order in a non-split classical quaternion algebra H(K) over an imaginary quadratic extension K of the rationals. We then apply this method to obtain a presentation for the unit group of H(Z[(1+root-7)/(2)]). As a consequence a presentation is discovered for the orthogonal group SO3(Z[(1+root-7)/(2)]). These results provide the first examples of a characterization of the unit group of some group rings that have an epimorphic image that is an order in a non-commutative division algebra that is not a totally definite quaternion algebra.


Item Type:Article
Uncontrolled Keywords:Algorithms; Finite sets of generators; Unit groups; Orders; quaternion algebras; Presentations
Subjects:Sciences > Mathematics > Group Theory
ID Code:14942
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Deposited On:20 Apr 2012 11:51
Last Modified:06 Feb 2014 10:12

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