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

2013/07/08 by Xie, BaoHua, Wang, JieYan, Jiang, YuePing
#Complex Variables (math.CV) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1307.2113

Abstract

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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