Quaternion Algebras, Arithmetic Kleinian Groups and Z-lattices
نویسندگان
چکیده
Let K be a quadratic extension of Q, B a quaternion algebra over Q and A = B ⊗Q K. Let O be a maximal order in A extending an order in B. The projective norm one group PO1 is shown to be isomorphic to the spinorial kernel group O′(L), for an explicitly determined quadratic Z-lattice L of rank four, in several general situations. In other cases, only the local structures of O and L are given at each prime. Both definite and indefinite lattices are covered. Some results for quadratic global field extensions K/F and maximal S-orders are given. There is a description of the F -quaternion subalgebras of A, and also of their norm one groups as stabilizer subgroups and as unitary groups. Conjugacy classes of the Fuchsian subgroups of PO1 corresponding to stabilizer subgroups are studied.
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