论文标题
Vinberg算法的有效界限算术双曲晶格
Effective bounds for Vinberg's algorithm for arithmetic hyperbolic lattices
论文作者
论文摘要
一组双曲线$ n $空间的异构体被称为反射组，如果它是由双曲线超平面中的反射产生的。 Vinberg给出了一个半合理，用于在最简单类型的$ O（n，1）$的给定算术子组中找到最大反射sublattice。我们为Vinberg的半合理提供了有效的终止条件，它成为寻找最大反射sublattices的算法。证明的主要新成分是对于算术双曲甲板多面体的面孔数量的上限，就其体积而言。
A group of isometries of a hyperbolic $n$-space is called a reflection group if it is generated by reflections in hyperbolic hyperplanes. Vinberg gave a semi-algorithm for finding a maximal reflection sublattice in a given arithmetic subgroup of $O(n,1)$ of the simplest type. We provide an effective termination condition for Vinberg's semi-algorithm with which it becomes an algorithm for finding maximal reflection sublattices. The main new ingredient of the proof is an upper bound for the number of faces of an arithmetic hyperbolic Coxeter polyhedron in terms of its volume.
