Vol. 53, No. 2, 1974

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Quaternion orders associated with ternary lattices

Gordon L. Nipp

Vol. 53 (1974), No. 2, 525–537

It is advantageous for the study of the spinor genus of quaternion orders to realize each order as corresponding to a ternary lattice. In the two known correspondences, those of Eichler and Pall, the question of whether the mapping is onto or not is not considered. Peters has investigated the question for Eichler’s correspondence, and his results show that it is not onto. Pall’s correspondence, though onto, is only defined over the rational integers. In this article, a generalization to Dedekind domains of Pall’s correspondence is defined. Those orders which are images of ternary lattices under the correspondence are completely determined, and the relationship of this mapping to Eichler’s is examined.

Mathematical Subject Classification 2000
Primary: 10C05
Secondary: 15A66
Received: 25 March 1973
Revised: 12 February 1974
Published: 1 August 1974
Gordon L. Nipp