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TEST MAP AND DISCRETENESS IN SL(2, ℍ)

Part of: Other groups of matrices Real and complex geometry

Published online by Cambridge University Press:  07 August 2018

KRISHNENDU GONGOPADHYAY Open the ORCID record for KRISHNENDU GONGOPADHYAY [Opens in a new window] ,
ABHISHEK MUKHERJEE  and
SUJIT KUMAR SARDAR
KRISHNENDU GONGOPADHYAY*
Affiliation:
Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, Sector 81, SAS Nagar, Punjab 140306, India e-mail: krishnendu@iisermohali.ac.in, krishnendug@gmail.com
ABHISHEK MUKHERJEE*
Affiliation:
Kalna College, Kalna, Dist. Burdwan 713409, West BengalDepartment of Mathematics, Jadavpur University, Jadavpur 700032, Kolkata e-mail: abhimukherjee.math10@gmail.com
SUJIT KUMAR SARDAR*
Affiliation:
Department of Mathematics, Jadavpur University, Jadavpur 700032, Kolkata e-mail: sksardar@math.jdvu.ac.in
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Abstract

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Let ℍ be the division ring of real quaternions. Let SL(2, ℍ) be the group of 2 × 2 quaternionic matrices $A={\scriptsize{(\begin{array}{l@{\quad}l} a & b \\ c & d \end{array})}}$ with quaternionic determinant det A = |ad − aca−1b| = 1. This group acts by the orientation-preserving isometries of the five-dimensional real hyperbolic space. We obtain discreteness criteria for Zariski-dense subgroups of SL(2, ℍ).

MSC classification

Primary: 20H10: Fuchsian groups and their generalizations
Secondary: 51M10: Hyperbolic and elliptic geometries (general) and generalizations 20H25: Other matrix groups over rings
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 3 , September 2019 , pp. 523 - 533
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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