GENERATORS OF THE GAUSS-PICARD MODULAR GROUP IN THREE COMPLEX DIMENSIONS

被引：2
|
作者：
Xie, BaoHua [1 ]
Wang, JieYan [2 ]
Jiang, YuePing [1 ]
机构：
[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China
[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
来源：
PACIFIC JOURNAL OF MATHEMATICS | 2015年 / 273卷 / 01期
关键词：
complex hyperbolic space; Picard modular groups; generators; REFLECTION GROUPS; HYPERBOLIC SPACE;
D O I：
10.2140/pjm.2015.273.197
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we will describe a method to obtain the generators system of Gauss-Picard modular group PU(3, 1; Z[i]). More precisely, we will show that PU(3, 1; Z[i]) can be generated by five given transformations: two Heisenberg translations, two Heisenberg rotations and one involution. Indeed, the same method works for the other higher-dimensional Euclidean Picard modular groups.
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页码：197 / 211
页数：15
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