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Rotations and units in quaternion algebras

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Corrales Rodrigáñez, Carmen (2012) Rotations and units in quaternion algebras. Journal of Number Theory, 132 (5). pp. 888-895. ISSN ISSN 1096-1658

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022314X12000078


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Abstract

Unit groups of orders in quaternion algebras over number fields provide important examples of non-commutative arithmetic groups. Let K = Q(d ) be a quadratic field with d < 0 a squarefree integer such that d ≡ 1(mod 8), and let R be its ring of integers. In this note we study, through its representation in SO3(R), the group of units of several orders in the quaternion algebra over K with basis {1, i, j,k} satisfying the relations i2 =j2 =−1, i j =−ji =k.


Item Type:Article
Uncontrolled Keywords:Quaternion algebras; Quadratic fields; Special orthogonal group of the space of pure quaternions in a quaternion algebra over a quadratic field
Subjects:Sciences > Mathematics > Number theory
ID Code:20272
Deposited On:06 Mar 2013 14:39
Last Modified:04 Apr 2016 10:07

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