Generators for the Euclidean Picard Modular Groups
Generators for the Euclidean Picard Modular Groups
复制标题
欧几里得皮卡德模群的生成器
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Tie
中科院分区：
文献类型：
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作者：
Tie
本文的目的是证明五个显式给定的变换，旋转，两个螺旋海森堡旋转，垂直平移和对合生成系数在二次虚数域的整数欧氏环中的欧氏Picard模群。通过对海森堡群中基本区域的组合学分析，得到了各向同性子群之间的关系。
The goal of this article is to show that five explicitly given transformations, a rotation, two screw Heisenberg rotations, a vertical translation and an involution generate the Euclidean Picard modular groups with coefficient in the Euclidean ring of integers of a quadratic imaginary number field. We also obtain the relations of the isotropy subgroup by analysis of the combinatorics of the fundamental domain in Heisenberg group.