Publication: Rotations and units in quaternion algebras
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Publication Date
2012
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Elsevier
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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.
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M. Alsina, P. Bayer, Quaternion Orders, Quadratic Forms and Shimura Curves, CRM Monogr.Ser.,vol.22,Amer.Math.Soc.,2004.
A.F. Beardon, The Geometry of Discrete Groups, Springer, Berlin, 1983.
H. Cohn, G. Pall, Sums of four squares in a quadratic ring, Trans. Amer. Math. Soc. 105 (3) (1962) 536–556.
C. Corrales-Rodrigáñez, G. Leal, E. Jespers, A. del Río, On the group of units of an order in a non-split quaternion algebra,Adv. Math. 186 (2004) 498–524.
J. Elstrodt, F. Grunewald, J. Mennicke, Groups Acting on Hyperbolic Space, Harmonic Analysis and Number Theory, Springer,1998.
B. Fine, The Algebraic Structure of the Bianchi Groups,Marcel Dekker, 1989.
A.J. Hahn, O.T. O’Meara, The Classical Groups and K-Theory, Grundlehren Math. Wiss., vol. 291, Springer-Verlag, 1989.
T.Y. Lam, Introduction to Quadratic Forms over Fields,Grad. Stud. Math., vol. 67, Amer. Math. Soc., 2005.
B. Maskit, Kleinian Groups, Springer, 1988.
H. Poincaré, Mémoire sur le groupes, kleinéens, Acta Math. 3 (1883) 49–92.
J. Voight, Computing Automorphic forms on Shimura curves over fields with arbitrary class number, in: Algorithmic Number Theory, Proceedings of ANTS IX, Nancy, France, 2010, in: Lecture Notes in Comput. Sci., vol. 6197, Springer, Berlin,2010, pp. 357–371.
A. Weil, Number Theory, an Approach Through History, Birkhäuser, Boston, 1984.