A Characterization of Gorenstein Orders in Quaternion Algebras

摘要

A characterization of Gorenstein orders in quaternion algebras is presented with orders corresponding by means of a natural construction, to lattices on the quadratic space consisting of quaternions with trace equal to 0 and with quadratic structure given by the reduced norm. This characterization gives a possibility to apply the theory of Gorenstein orders to lattices (quadratic forms) on ternary quadratic spaces. A generalization to arbitrary characterics of a classical result of Brandt about invertibility of submodules in quaternion algebras is given.