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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Algebraic characterization of isometries of the complex and the quaternionic hyperbolic $ 3$-spaces


Author: Krishnendu Gongopadhyay
Journal: Proc. Amer. Math. Soc. 141 (2013), 1017-1027
MSC (2010): Primary 51M10; Secondary 15B57, 53C35
Published electronically: July 26, 2012
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Abstract: Let $ \mathbf {H}^3_{\mathbb{F}}$ denote the three dimensional hyperbolic space over $ \mathbb{F}$, where $ \mathbb{F}$ denotes either the complex numbers $ \mathbb{C}$ or the quaternions $ \mathbb{H}$. We offer an algebraic characterization of isometries of $ \mathbf {H}^3_{\mathbb{F}}$.


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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, Mohali 140306, India
Email: krishnendug@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11422-4
PII: S 0002-9939(2012)11422-4
Keywords: Isometry, complex and quaternionic hyperbolic space, classification
Received by editor(s): March 31, 2011
Received by editor(s) in revised form: July 24, 2011
Published electronically: July 26, 2012
Additional Notes: The author gratefully acknowledges the support of SERC-DST FAST grant SR/FTP/MS-004/2010.
Communicated by: Michael Wolf
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.