Jorgensen's inequality for quaternionic hyperbolic n-space

2009/06/08 by Wensheng Cao, Cao, Wensheng
Mathematics · #20H10 #22E40 #57S30 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic and Geometric Analysis #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications #math.AG #math.AT #msc:20H10 #msc:22E40 #msc:57S30

paper · pdf · doi:10.48550/arxiv.0906.1475

12 pages

openalex publication_date 2009/06/08 · arxiv created 2010/01/23 · arxiv updated 2010/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Jorgensen's inequality gives a necessary condition for a non-elementary two generator group of isometries of real hyperbolic 2-space to be discrete. We give analogues of Jorgensen's inequality for non-elementary groups of isometries of quaternionic hyperbolic n-space generated by two elements, one of which is loxodromic.

Citations

• Quaternions and matrices of quaternions

Related

• Jorgensen's inequality for quternionic hyperbolic space with elliptic elements
• Jorgensen's Inequalities and Collars in n-dimensional Quaternionic Hyperbolic Space
• On discreteness of subgroups of quaternionic hyperbolic isometries
• Totally Geodesic Spectra of Quaternionic Hyperbolic Orbifolds
• Test map and Discreteness in SL(2, \mathbb H)