## Classification of quaternionic hyperbolic isometries

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- by Krishnendu Gongopadhyay and Shiv Parsad
- Conform. Geom. Dyn.
**17**(2013), 68-76 - DOI: https://doi.org/10.1090/S1088-4173-2013-00256-7
- 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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## Bibliographic 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
- MR Author ID: 866190
- 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
- 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. - © Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn.
**17**(2013), 68-76 - MSC (2010): Primary 51M10; Secondary 15B33, 15B57, 20G20
- DOI: https://doi.org/10.1090/S1088-4173-2013-00256-7
- MathSciNet review: 3049200