Notes on Discrete Subgroups of Möbius Transformations

Proceedings Mathematical Sciences

Hua Wang²  Yueping Jiang³  Wensheng Cao¹ 

[1] School of Mathematics and Computational Science, Wuyi University, Jiangmen, Guangdong 00, People’s Republic of China$$;Department of Mathematics, Changsha University of Science and Technology, Changsha, Hunan 00, People’s Republic of China$$;Department of Applied Mathematics, Hunan University, Changsha 00, People’s Republic of China$$

关键词: Jørgensen’s inequality;    quaternionic hyperbolic space;    embedding.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Jørgensen’s inequality gives a necessary condition for a nonelementary two generator subgroup of $SL(2,mathbb{C})$ to be discrete. By embedding $SL(2,mathbb{C})$ into $Û(1,1;mathbb{H})$, we obtain a new type of Jørgensen’s inequality, which is in terms of the coefficients of involved isometries. We provide an example to show that this result gives an improvement over the classical Jørgensen’s inequality.

【 授权许可】

Unknown