论文标题
扭曲的欧几里得算法：数字理论和几何形状的应用
The Twisted Euclidean Algorithm: Applications to Number Theory and Geometry
论文作者
论文摘要
我们介绍了配备有事的环的欧几里得算法的概括，并完全列举了所有具有正交相关性的确定的，理性的季节代数，这些代数是正交相关的，这些代数承认了这种算法。我们提供两个应用程序：首先，任何接纳此类算法的订单具有1级；其次，我们展示了这种算法的存在如何与构造双曲线4空间等轴测组的kleinian子组的显式dirichlet域的问题有关。
We introduce a generalization of the Euclidean algorithm for rings equipped with an involution, and completely enumerate all isomorphism classes of orders over definite, rational quaternion algebras equipped with an orthogonal involution that admit such an algorithm. We give two applications: first, any order that admits such an algorithm has class number 1; second, we show how the existence of such an algorithm relates to the problem of constructing explicit Dirichlet domains for Kleinian subgroups of the isometry group of hyperbolic 4-space.
