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      Permanent link:
      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

       

      Hua Wang1 Yueping Jiang2 Wensheng Cao3

      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

    • Dates

       
      Published
      May 2013
      Manuscript received
      12 January 2012
      Manuscript revised
      27 April 2012

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