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Generators of the Picard Modular Group $SU(2,1;\\mathbb{Z}[\\sqrt{2}i])$
Xiao Yingqing * #,Jiang yueping
College of Mathematics and Economics, Hunan University
*Correspondence author
#Submitted by
Subject:
Funding: 国家自然科学基金,教育部博士点基金（No.10761059,200605322023）
Opened online:21 January 2010
Accepted by: none
Citation: Xiao Yingqing,Jiang yueping.Generators of the Picard Modular Group $SU(2,1;\\mathbb{Z}[\\sqrt{2}i])$[OL]. [21 January 2010] http://en.paper.edu.cn/en_releasepaper/content/39299
 
 
Recently, Falbel,Francsics, Lax, Parker proved that four explicitly given transformations generate the Picard modular group $SU(2,1; \\mathcal{O}_1)$. They conjecture that their method can be extended to the other Euclidean rings $\\mathcal{O}_d$. In this note, we study the case of $d=2$ and obtain five explicitly given transformations can generate the Picard modular group $SU(2,1; \\mathcal{O}_2)$.
Keywords:complex hyperbolic space;picard modular group;generator
 
 
 

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