Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups
We obtain an analogue of Jørgensen's inequality in quaternionic hyperbolic space. As an application, we prove that if the r-generator quaternionic Kleinian group satisfies I-condition, then its algebraic limit is also a quaternionic Kleinian group. Our results are generalizations of the counter...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/684594 |
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| author | Huani Qin Yueping Jiang Wensheng Cao |
| author_facet | Huani Qin Yueping Jiang Wensheng Cao |
| author_sort | Huani Qin |
| collection | DOAJ |
| description | We obtain an analogue of Jørgensen's inequality in quaternionic hyperbolic space. As an application, we prove that if the r-generator quaternionic Kleinian group satisfies I-condition, then its algebraic limit is also a quaternionic Kleinian group. Our results are generalizations of the counterparts in the n-dimensional real hyperbolic space. |
| format | Article |
| id | doaj-art-f550a63344e6420a95314e30f73666d7 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f550a63344e6420a95314e30f73666d72025-02-03T01:23:36ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/684594684594Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry GroupsHuani Qin0Yueping Jiang1Wensheng Cao2College of Applied Mathematics, Hunan University, Changsha 410082, ChinaCollege of Applied Mathematics, Hunan University, Changsha 410082, ChinaCollege of Mathematics and Computation Science, Wuyi University, Jiangmen 529020, ChinaWe obtain an analogue of Jørgensen's inequality in quaternionic hyperbolic space. As an application, we prove that if the r-generator quaternionic Kleinian group satisfies I-condition, then its algebraic limit is also a quaternionic Kleinian group. Our results are generalizations of the counterparts in the n-dimensional real hyperbolic space.http://dx.doi.org/10.1155/2014/684594 |
| spellingShingle | Huani Qin Yueping Jiang Wensheng Cao Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups Abstract and Applied Analysis |
| title | Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups |
| title_full | Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups |
| title_fullStr | Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups |
| title_full_unstemmed | Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups |
| title_short | Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups |
| title_sort | jorgensen s inequality and algebraic convergence theorem in quaternionic hyperbolic isometry groups |
| url | http://dx.doi.org/10.1155/2014/684594 |
| work_keys_str_mv | AT huaniqin jørgensensinequalityandalgebraicconvergencetheoreminquaternionichyperbolicisometrygroups AT yuepingjiang jørgensensinequalityandalgebraicconvergencetheoreminquaternionichyperbolicisometrygroups AT wenshengcao jørgensensinequalityandalgebraicconvergencetheoreminquaternionichyperbolicisometrygroups |