• Notes on Discrete Subgroups of Möbius Transformations

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/123/02/0245-0251

• # Keywords

Jørgensen’s inequality; quaternionic hyperbolic space; embedding.

• # Abstract

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.

• # Author Affiliations

1. Department of Mathematics, Changsha University of Science and Technology, Changsha, Hunan 410076, People’s Republic of China
2. Department of Applied Mathematics, Hunan University, Changsha 410082, People’s Republic of China
3. School of Mathematics and Computational Science, Wuyi University, Jiangmen, Guangdong 529020, People’s Republic of China

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
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• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019

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