Vol. 273, No. 1, 2015

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Generators of the Gauss–Picard modular group in three complex dimensions

BaoHua Xie, JieYan Wang and YuePing Jiang

Vol. 273 (2015), No. 1, 197–211
Abstract

In this paper, we will describe a method to obtain the generators system of Gauss–Picard modular group PU(3,1; [i]). More precisely, we will show that PU(3,1; [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.

Keywords
complex hyperbolic space, Picard modular groups, generators
Mathematical Subject Classification 2010
Primary: 32M05, 22E40
Secondary: 32M15
Milestones
Received: 11 January 2014
Revised: 27 April 2014
Accepted: 1 June 2014
Published: 6 December 2014
Authors
BaoHua Xie
College of Mathematics and Econometrics
Hunan University
Changsha, 410082
China
JieYan Wang
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
Beijing, 100190
China
YuePing Jiang
College of Mathematics and Econometrics
Hunan University
Changsha, 410082
China