扭曲的Euclidean Algorithm：在数论和几何中的应用
The Twisted Euclidean Algorithm: Applications to Number Theory and Geometry
摘要：
我们介绍了一个推广的欧几里得算法的环配备了一个对合，并完全列举了所有同构类的订单上确定，有理四元数代数配备了一个正交对合，承认这样一个算法。我们给出两个应用：首先，任何顺序，承认这样一个算法有类数1; 2其次，我们显示了如何存在这样一个算法涉及到的问题，构造显式Dirichlet域的Kleinian子群的等距群的双曲4-空间。
英文摘要：
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.
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