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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173

Classification of quaternionic hyperbolic isometries


Authors: Krishnendu Gongopadhyay and Shiv Parsad
Journal: Conform. Geom. Dyn. 17 (2013), 68-76
MSC (2010): Primary 51M10; Secondary 15B33, 15B57, 20G20
Published electronically: May 6, 2013
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Abstract: Let $ \mathbb{F}$ denote either the complex numbers $ \mathbb{C}$ or the quaternions $ \mathbb{H}$. Let $ \mathbf {H}_{\mathbb{F}}^n$ denote the $ n$-dimensional hyperbolic space over $ \mathbb{F}$. We obtain algebraic criteria to classify the isometries of $ \mathbf {H}_{\mathbb{F}}^n$. This generalizes the work in Geom. Dedicata 157 (2012), 23-39 and Proc. Amer. Math. Soc. 141 (2013), 1017-1027, to isometries of arbitrary dimensional quaternionic hyperbolic space. As a corollary, a characterization of isometries of $ \mathbf {H}_{\mathbb{C}}^n$ is also obtained.


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Additional Information

Krishnendu Gongopadhyay
Affiliation: Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, S.A.S. Nagar, Sector 81, P. O. Manauli, Pin 140306, India
Email: krishnendug@gmail.com

Shiv Parsad
Affiliation: Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, S.A.S. Nagar, Sector 81, P. O. Manauli, Pin 140306, India
Email: parsad.shiv@gmail.com

DOI: http://dx.doi.org/10.1090/S1088-4173-2013-00256-7
PII: S 1088-4173(2013)00256-7
Keywords: Complex and quaternionic hyperbolic space, classification of isometries
Received by editor(s): August 1, 2012
Published electronically: May 6, 2013
Additional Notes: The first author acknowledges the support of SERC-DST FAST grant SR/FTP/MS-004/2010.
The second author acknowledges the support of CSIR research fellowship.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.