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Title: | On discreteness of subgroups of quaternionic hyperbolic isometries |
Authors: | Gongopadhyay, Krishnendu |
Keywords: | Hyperbolic space Jørgensen inequality Discreteness Quaternions |
Issue Date: | 2020 |
Publisher: | Cambridge University Press |
Citation: | Bulletin of the Australian Mathematical Society 101(2), pp. 283-293 |
Abstract: | Let HnH denote the n -dimensional quaternionic hyperbolic space. The linear group Sp(n,1) acts on HnH by isometries. A subgroup G of Sp(n,1) is called Zariski dense if it neither fixes a point on HnH∪∂HnH nor preserves a totally geodesic subspace of HnH . We prove that a Zariski dense subgroup G of Sp(n,1) is discrete if for every loxodromic element g∈G the two-generator subgroup ⟨f,gfg−1⟩ is discrete, where the generator f∈Sp(n,1) is a certain fixed element not necessarily from G . |
Description: | Only IISERM authors are available in the record. |
URI: | https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/abs/on-discreteness-of-subgroups-of-quaternionic-hyperbolic-isometries/50C80C47EAB520FCA9ACA50BDEE667B4 http://hdl.handle.net/123456789/3346 |
Appears in Collections: | Research Articles |
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