arXiv 1307.21132013-07-08math.CVmath.GR

三维复Gauss-Picard模群的生成元

Generators of the Gauss-Picard modular groups in three complex dimensions

BaoHua Xie, JieYan Wang, YuePing Jiang

备注：: 14pages,2 figures. arXiv admin note: substantial text overlap with arXiv:1111.6796; and text overlap with arXiv:1006.3331 by other authors

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摘要：

本文证明了三维Gauss-Picard模群PU（3，1;Z[i]）可以由五个给定的变换生成：两个Heisenberg平移，两个Heisenberg旋转和一个对合.事实上，我们的方法可能适用于其他高维欧几里德-皮卡德模群。

英文摘要：

In this paper, we prove that the Gauss--Picard modular group PU(3,1;Z[i])in three complex dimensions can be generated by five given transformations: two Heisenberg translations, two Heisenberg rotations and an involution. Indeed, our method may work for the other higher dimensional Euclidean--Picard modular groups.

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