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

Gongopadhyay, Krishnendu

doi:10.1090/S0002-9939-2012-11422-4

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

Author: Krishnendu Gongopadhyay
Journal: Proc. Amer. Math. Soc. 141 (2013), 1017-1027
MSC (2010): Primary 51M10; Secondary 15B57, 53C35
Posted: 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
Posted: 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.

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