Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups

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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Main Authors: Huani Qin, Yueping Jiang, Wensheng Cao
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/684594
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spelling doaj-f550a63344e6420a95314e30f73666d72020-11-24T22:17:01ZengHindawi LimitedAbstract 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
collection DOAJ
language English
format Article
sources DOAJ
author Huani Qin
Yueping Jiang
Wensheng Cao
spellingShingle Huani Qin
Yueping Jiang
Wensheng Cao
Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups
Abstract and Applied Analysis
author_facet Huani Qin
Yueping Jiang
Wensheng Cao
author_sort Huani Qin
title 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_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_sort jørgensen’s inequality and algebraic convergence theorem in quaternionic hyperbolic isometry groups
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
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.
url http://dx.doi.org/10.1155/2014/684594
work_keys_str_mv AT huaniqin jørgensensinequalityandalgebraicconvergencetheoreminquaternionichyperbolicisometrygroups
AT yuepingjiang jørgensensinequalityandalgebraicconvergencetheoreminquaternionichyperbolicisometrygroups
AT wenshengcao jørgensensinequalityandalgebraicconvergencetheoreminquaternionichyperbolicisometrygroups
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